Reconstruction Method of a Computed Tomographic Image From a Few X-Ray Projections

1. A reconstructions method of a computed tomographic image from a few X-ray projections comprising: (a) projecting X-rays from two desired directions toward tested tissue of a body for producing first and second X-ray projectional distributions of X-rays which have passed through the tested tissue; (b) measuring the values d.sub.k (k is natural number) of X-ray density on said first X-ray projectional distribution at a plurality of positions spaced apart from each other from one end of said first X-ray projectional distribution toward the other end thereof, and at the same time measuring the values d.sub.k ' (k' is natural number) of X-ray density on said second X-ray projectional distribution at a plurality of positions spaced apart from each other from one end of said second X-ray projectional distribution toward the other end thereof, where said plurality of positions spaced apart from each other on the first and second X-ray projectional distributions for measurement of the values d.sub.k and d.sub.k, of X-ray density are selected according to the following three criteria, (i) that the tomographic plane of the tested tissue of a body to be reconstructed is expressed by a pseudo-tomographic plane which is constituted collectively by mn pieces of picture elements, with m pieces of picture elements in a row and n in a column (both m and n are natural numbers), which are formed by dividing said tomographic plane of the tested tissue of a body into small sections and each of which has a single piece of X-ray density information, and that said pseudo-tomographic plane is placed between an X-ray source and said two X-ray projectional distributions, (ii) that said pseudo-tomographic plane is divided into a first part of a plane constructed collectively by said picture elements with i pieces in a row (i is natural number, i< m) and n picture elements in a column and a second part of a plane constituted collectively by said picture elements with (m-i) pieces in a row and n pieces in a column, (iii) that n rows, each of which is constituted by m pieces of picture elements are numbered in order 1,2, . . . , n from the left and that said m pieces of picture elements in each row are numbered respectively 1,2, . . . , m; m+1, m+2, . . . , 2m; . . . ; (n-1)m+1, (n-1)m+2, . . . mn from the side of said x-ray source toward the side of said two X-ray projectional distributions in order and that at least mn X-ray beams passing through said pseudo-tomographic plane from two directions comprise the first group of X-ray beams passing through respectively the left lower corner of each picture element in said first part of a plane and the second group of X-ray beams passing through respectively the left upper corner of each picture element in said second part of a plane, and said plurality of positions spaced apart from each other on said two X-ray projectional distributions for measurement of the values d.sub.k and d.sub.k' of X-ray density correspond to the positions on said two X-ray projectional distributions which have X-ray density information to be obtained by passing said X-ray beams through said pseudo-tomographic plane; (c) calculating the X-ray absorption coefficient .mu..sub.t (t=1,2, . . . , mn and t is a natural number) of each of mn pieces of picture elements based on the X-ray density values d.sub.k and d.sub.k' measured in step (b) and length of the X-ray beams passing through each of the picture elements; (d) reconstructing the computed tomographic image of said tested tissue of a body, where the picture elements having respective X-ray absorption coefficients .mu..sub.1,.mu..sub.2, . . . , .mu..sub.mn calculated in step (c) are positioned at the locations of said picture elements numbered 1,2, . . . , mn of the pseudo-tomographic plane and wherein the complete collection of picture elements located in the m.times.n array constitute the reconstructed computed tomographic plane of the tested tissue of body.

2. A reconstruction method of a computed tomographic image from a few X-ray projections according to claim 1, wherein neighboring measuring positions on said X-ray projectional distributions are equally spaced apart.

3. A reconstruction method of a computed tomographic image according to claim 1, comprising the step of displaying the m.times.n array of picture elements in order to display the internal structure of said tested tissue of a body.

4. A reconstruction method of a computed tomographic image from a few X-ray projections comprising: (a) projecting X-rays from two symmetrical desired directions (.theta..sub.1, .theta..sub.2) toward tested tissue of a body for producing first and second X-ray projectional distributions D.sub.1, D.sub.2 of X-rays which have passed through the tested tissue; (b) measuring the values d.sub.k (1) (k(1) is a natural number) of X-ray density on said first X-ray projectional distribution D.sub.1 at mn/2 (m and n are natural numbers and the product of m and n is an even number) positions spaced apart from each other from one end of said first X-ray projectional distribution D.sub.1 toward the other end thereof, and at the same time measuring the values d.sub.k (2) (k(2) is a natural number) of X-ray density on said second X-ray projectional distribution D.sub.2 at mn/2 positions spaced apart from each other from one end of said second X-ray projectional distribution D.sub.2 toward the other end thereof, where said mn/2 positions spaced apart from each other on the first and second X-ray projectional distributions D.sub.1, D.sub.2 for measurement of the values d.sub.k (1) and d.sub.k (2) of X-ray density are selected according to the following three criteria, (i) that the tomographic plane of the tested tissue of a body to be reconstructed is expressed by a pseudo-tomographic plane which is constituted collectively by mn pieces of square picture elements, with m pieces of picture elements in a row and n in a column (both m and n are natural numbers), which are formed by dividing said tomographic plane of the tested tissue of a body into small sections and each of which has a single piece of X-ray density information, and that said pseudo-tomographic plane is placed between an X-ray source and said two X-ray projectional distributions D.sub.1, D.sub.2 (ii) that said pseudo-tomographic plane is divided into a first part of a plane and a second part of a plane which are constituted collectively by said picture elements with m/2 pieces in a row and n pieces in a column, respectively, (iii) that n rows, each of which is constituted by m pieces of picture elements are numbered in order 1, 2, . . . , n from the left and that said m pieces of picture elements in each row are numbered respectively 1, 2, . . . , m; m+1, m+2, . . . , 2m . . . ; (n-1)m+1, (n-1)m+2, . . . mn from the side of said X-ray source toward the side of said two X-ray projectional distributions D.sub.1, D.sub.2 in order and that mn X-ray beams passing through said pseudo-tomographic plane from two directions comprise the first group of X-ray beams which is constituted by mn/2 X-ray beams in a direction of .theta..sub.1, passing through respectively the left lower corner of each picture element in said first part of a plane and the second group of X-ray beams which is constituted by mn/2 X-ray beams in a direction of .theta..sub.2 passing through respectively the left upper corner of each picture element in said second part of a plane, and said mn/2 positions spaced apart from each other on said two X-ray projectional distributions D.sub.1, D.sub.2 for measurement of the values d.sub.k (1) and d.sub.k (2) of X-ray density correspond to the positions on said two X-ray projectional distributions D.sub.1, D.sub.2 which have X-ray density information to be obtained by passing said X-ray beams through said pseudo-tomographic plane, .theta..sub.1 indicates the angle at which each X-ray beam of the first group crosses with the base of each picture element in the first part of a plane, and .theta..sub.1 =tan.sup.-1(m/2), and .theta..sub.2 indicates the angle at which each X-ray beam of the second group crosses with the base of each picture element in the second part of a plane, and .theta..sub.2 = -tan.sup.-1(m/2) ; (c) calculating X-ray absorption coefficient .mu..sub.t (t=1, 2, . . . , mn and t is a natural number) of each of mn pieces of picture elements in accordance with the following equations based on the X-ray density values d.sub.k (1) and d.sub.k (2) measured in step (b) and length of the X-ray beams passing through each of the picture elements, ##EQU41## L is a square matrix of dimensions mn.times.mn, T indicates a matrix transpose and .alpha. is a length of an X-ray beam passing through each picture element from directions of .theta..sub.1 and .theta..sub.2 ; (d) reconstructing the computed tomographic image of said tested tissue of a body, where the picture elements having respective X-ray absorption coefficients .mu..sub.1, .mu..sub.2, . . . , .mu..sub.mn calculates in step (c) are positioned at the locations of said picture elements numbered 1, 2, . . . , mn of the pseudo-tomographic plane and wherein the complete collection of picture elements located in the m=n array constitute the reconstructed computed tomographic plane of the tested tissue of a body.

5. A reconstruction method of a computed tomographic image from a few X-ray projections comprising: (a) projecting X-rays from two symmetrical desired directions (.theta..sub.3, .theta..sub.4) toward tested tissue of a body for producing first and second X-ray projectional distributions D.sub.3, D.sub.4 of X-rays which have passed through the tested tissue; (b) measuring the values d.sub.k (3) (k(3) is a natural number) of X-ray density on said first X-ray projectional distribution D.sub.3 at mn/2 (m and n are natural numbers and the product of m and n is an even number) positions spaced apart from each other from one end of said first X-ray projectional distribution D.sub.3 toward the other end thereof, and at the same time measuring the values d.sub.k (4) (k(4) is a natural number) of X-ray density on said second X-ray projectional distribution D.sub.4 at mn/2 positions spaced apart from each other from one end of said second X-ray projectional distribution D.sub.4 toward the other end thereof, where said mn/2 positions spaced apart from each other on the first and second X-ray projectional distributions D.sub.3, D.sub.4 for measurement of the valves d.sub.k (3) and d.sub.k (4) of X-ray density are selected according to the following three criteria, (i) that the tomographic plane of the tested tissue of a body to be reconstructed is expressed by a pseudo-tomographic plane which is constituted collectively by mn pieces of square picture elements, with m pieces of picture elements in a row and n in a column (both m and n are natural numbers), which are formed by dividing said tomographic plane of the tested tissue of a body into small sections and each of which has a single piece of X-ray density information, and that said pseudo-tomographic plane is placed between an X-ray source and said two X-ray projectional distributions D.sub.3, D.sub.4, (ii) that said pseudo-tomographic plane is divided into a first part of a plane and a second part of a plane which are constituted collectively by said picture elements with m/2 pieces in a row and n pieces in a column respectively, (iii) that n rows, each of which is constituted by m pieces of picture elements are numbered in order 1, 2, . . . , n from the left and that said m pieces of picture elements in each row are numbered respectively 1, 2, . . . m; m+1, m+2, . . . , 2 m; . . . ; (n-1)m+1, (n-1)m+2, . . . mn from the side of said X-ray source toward the side of said two X-ray projectional distributions D.sub.3, D.sub.4 in order and that mn X-ray beams passing through said pseudo-tomographic plane from two directions comprise the first group of X-ray beams which is constituted by mn/2 X-ray beams in a direction of .theta..sub.3, passing through respectively the left lower corner of each picture element in said first part of a plane and the second group of X-ray beams which is constituted by mn/2 X-ray beams in a direction of .theta..sub.4 passing through respectively the left upper corner of each picture element in said second part of a plane, and said mn/2 positions spaced apart from each other on said two X-ray projectional distributions D.sub.3, D.sub.4 for measurement of the values d.sub.k (3) and d.sub.k (4) of X-ray density correspond to the positions on said two X-ray projectional distributions which have X-ray density information to be obtained by passing said X-ray beams through said pseudo-tomographic plane, .theta..sub.3 indicates the angle at which each X-ray beam of the first group crosses with the base of each picture element in the first part of a plane, and .theta..sub.3 =tan.sup.-1 m and .theta..sub.4 indicates the angle at which each X-ray beam of the second group crosses with the base of each picture element in the second part of a plane, and .theta..sub.4 =-tan.sup.-1 m; (c) calculating X-ray absorption coefficient .mu..sub.t (t=1, 2, . . . , mn and t is a natural number) of each of mn pieces of picture elements in accordance with the following equations based of the X-ray density values d.sub.k (3) and d.sub.k (4) measured in step (b) and length of the X-ray beams passing through each of the picture elements, ##EQU42## L is a square matrix of dimension mn.times.mn, T indicates a matrix transpose and .alpha. is a length of an X-ray beam passing through each picture element from directions of .theta..sub.3, and .theta..sub.4 ; (d) reconstructing the computed tomographic image of said tested tissue of a body, where the picture elements having respective X-ray absorption coefficients .mu..sub.1, .mu..sub.2, . . . , .mu..sub.mn calculated in step (c) are positioned at the locations of said picture elements numbered 1, 2, . . . , mn of the pseudo-tomographic plane and wherein the complete collection of picture elements located in the m.times.n array constitute the reconstructed computed tomographic plane of the tested tissue of a body.

6. A reconstruction method of a computed tomographic image from a few X-ray projections comprising: (a) projecting X-rays from two symmetrical desired directions (.theta..sub.1, .theta..sub.2) toward tested tissue of a body for producing first and second X-ray projectional distributions D.sub.1, D.sub.2 of X-rays which have passed through the tested tissue; (b) measuring the values d.sub.k (1) (k(1) is a natural number, k(1)=1, 2, . . . , m/2) of X-ray density on said first X-ray projectional distribution D.sub.1 at m/2 (m is a natural number) positions spaced apart from each other from one end of said first X-ray projectional distribution D.sub.1 toward the other end thereof, and at the same time measuring the values d.sub.k (2) (k(2) is a natural number, k(2)=1, 2, . . . , m/2) of X-ray density on said second X-ray projectional distribution D.sub.2 at m/2 positions spaced apart from each other from one end of said second X-ray projectional distribution D.sub.2 toward the other end thereof, where said m/2 positions spaced apart from each other on the first and second X-ray projectional distributions D.sub.1, D.sub.2 for measurement of the values d.sub.k (1) and d.sub.k (2) of X-ray density are selected according to the following three criteria, (i) that the tomographic plane of the tested tissue of a body to be reconstructed is expressed by a pseudo-tomographic plane which is constituted collectively by mn pieces of square picture elements, with m pieces of picture elements in a row and n in a column (both m and n are natural numbers), which are formed by dividing said tomographic plane of the tested tissue of a body into small sections and each of which has a single piece of X-ray density information, and that said pseudo-tomographic plane is placed between an X-ray source and said two X-ray projectional distributions D.sub.1, D.sub.2, (ii) that said pseudo-tomographic plane is divided into a first part of a plane and a second part of a plane which are constituted collectively by said picture elements with m/2 pieces in a row and n pieces in a column, respectively, (iii) that n rows, each of which is constituted by m pieces of picture elements are numbered in order 1, 2, . . . , n from the left and that said m pieces of picture elements in each row are numbered respectively 1, 2, . . . , m; m+1, m+2, . . . , 2m; . . . ; (n-1)m+1, (n-1)m+2, . . . mn from the side of said X-ray source toward the side of said two X-ray projectional distributions D.sub.1, D.sub.2 in order and that mn X-ray beams passing through said pseudo-tomographic plane from two directions comprise the first group of X-ray beams which is constituted by mn/2 X-ray beams in a direction of .theta..sub.1, passing through respectively the left lower corner of each picture element in said first part of a plane and the second group of X-ray beams which is constituted by mn/2 X-ray beams in a direction of .theta..sub.2 passing through respectively the left upper corner of each picture element in said second part of a plane, and said m/2 positions spaced apart from each other on said two X-ray projectional distributions D.sub.1, D.sub.2 for measurement of the values d.sub.k (1) and d.sub.k (2) of X-ray density correspond to the positions on said two X-ray projectional distributions D.sub.1, D.sub.2 which have X-ray density information to be obtained by passing first m/2 X-ray beams through said pseudo-tomographic plane based on the abovementioned criteria, .theta..sub.1 indicates the angle at whih each X-ray beam of the first group crosses with the base of each picture element in the first part of a plane, and .theta..sub.1 -tan.sup.-1 m/2, and .theta..sub.2 indicates the angle at which each X-ray beam of the second group crosses with the base of each picture element in the second part of a plane, and .theta..sub.2 =-tan.sup.-1 m/2; (c) calculating X-ray absorption coefficient .mu..sub.t (t is a natural number, t=1, 2, . . . , m/2) of each of m/2 pieces of picture elements in the first part of a plane in accordance with the following equations based on the values d.sub.k (1) of X-ray density measured in step (b) and length of the X-ray beams in the direction of .theta..sub.1 passing through each picture element in the first part of a plane, and at the same time calculating X-ray absorption coefficient .mu..sub.t (t is a natural number, t=m/2+1, m/2+2, . . . ,m) of each of m/2 pieces of picture elements in the second part of a plane in accordance with the following equations based on the values d.sub.k (2) of X-ray density measured in step (b) and length of the X-ray beams in the direction of .theta..sub.2 passing through each picture element in the second part of plane, ##EQU43## L is a square matrix of dimension m.times.m, T indicates a matrix transpose and .alpha. is a length of an X-ray beam passing through each picture element from directions of .theta..sub.1, .theta..sub.2 ; (d) memorizing X-ray absorption coefficients .mu..sub.1 .about..mu..sub.m calculated in step (c); (e) measuring each of the values d.sub.k (1) (k(1) is a natural number, k(1)=m/2+1, m/2+2, . . . ,m) of X-ray density on said first X-ray projectional distribution D.sub.1 at the positions numbering m/2 spaced apart from each other from the (m/2+1) position from one end of said first X-ray projectional distribution D.sub.1 toward the other end thereof, and at the same time measuring each of the values d.sub.k (2) (k(2) is a natural number, k(2)=m/2+1, m/2+2, . . . , m) of X-ray density on said second X-ray projectional distribution D.sub.2 at the positions number m/2 spaced apart from each other from the (m/2+1) position from one end of said second X-ray projectional distribution D.sub.2 toward the other end thereof, where said positions numbering m/2 spaced apart from each other on said first X-ray projectional distribution D.sub.1 for measurement of the values d.sub.k (1) (k(1)=m/2+1, m/2+2, . . . ,m) of X-ray density are selected such that said positions number m/2 spaced apart from each other on said first X-ray projectional distribution D.sub.1 for measurement of the values d.sub.k (1) (k(1)=m/2+1, m/2+2, . . . , m) of X-ray density correspond to the positions on said first X-ray projectional distribution D.sub.1 which have X-ray density information obtained as a result of the m/2 X-ray beams passing through the left lower corner of each of the respective picture elements number (m+1) to 3m/2 passing through said first part of a plane based on the three criteria in step (b), and said positions numbering m/2 spaced apart from each other on said second X-ray projectional distribution D.sub.2 for measurement of the values d.sub.k (2) (k(2)=m/2+1, m/2+2, . . . , m) of X-ray density are selected such that said positions number m/2 spaced apart from each other on said second X-ray projectional distribution D.sub.2 for measurement of the values d.sub.k (2) (k(2)=m/2+1, m/2, . . . , m) of X-ray density correspond to the positions on said second X-ray projectional distribution D.sub.2 which have X-ray density information obtained as a result of the m/2 X-ray beams passing through the left upper corner of each of the respective picture elements numbered ##EQU44## to 2m passing through said second part of a plane based on the three criteria in step (b); (f) calculating the X-ray absorption coefficients .mu..sub.m+1 .about..mu..sub.3m/2 based on the X-ray absorption coefficients .mu..sub.1 .about..mu..sub.m calculated in step (c), the values d.sub.k (1) (k(1)=m/2+1, m/2+2, . . . , m) of X-ray density measured in step (e), and the length of X-ray beams passing through the picture elements numbered (m+1) to 3m/2 from the .theta..sub.1 direction, and at the same time, calculating the X-ray absorption coefficients .mu..sub.3m/2+1 .about..mu..sub.2m based on the X-ray absorption coefficients .mu..sub.1 .about..mu..sub.m calculated in step (c), the values d.sub.k (2) (k(2)=m/2+1, m/2+2, . . . , m) of X-ray density measured in step (e), and the length of X-ray beams passing through the picture elements numbered (3m/2+1) to 2m from the .theta..sub.2 direction, where the method of calculating the X-ray absorption coefficients .mu..sub.m+1 .about..mu..sub.2m is the same as in step (c) and the X-ray absorption coefficients .mu..sub.1 .about..mu..sub.m calculated in step (c) are selectively used; (g) memorizing the X-ray absorption coefficients .mu..sub.m+1 .about..mu..sub.2m calculated in step (f); (h) calculating the X-ray absorption coefficients .mu..sub.2m+1 .about..mu..sub.3m , .mu..sub.3m+1 .about..mu..sub.4m, . . . , .mu..sub.(n-1)m+1 .about..mu..sub.mn repeating substantially the same steps as steps (e), (f) and (g) and memorizing them; (i) reconstructing the computed tomographic image of said tested tissue of a body based on the X-ray absorption coefficients .mu..sub.1 .about..mu..sub.m, .mu..sub.m+1 .about..mu..sub.2m, . . . , .mu..sub.(n-1) m+1 .about..mu..sub.mn memorized in steps (d), (g) and (h), where the picture elements having respective X-ray absorption coefficcients .mu..sub.1, .mu..sub.2, . . . , .mu..sub.mn calculated in step (c), (f) and (h) are positioned at the locations of said picture elements number 1, 2, . . . , mn of the pseudo-tomographic plane and wherein the complete collection of picture elements located in the m.times.n array constitute the reconstructed computed tomographic plane of the tested tissue of body.

7. A reconstruction method of a computed tomographic image from a few X-ray projections comprising: (a) projecting X-rays from two symmetrical desired directions (.theta..sub.3, .theta..sub.4) toward tested tissue of a body for producing first and second X-ray projectional distributions D.sub.3, D.sub.4 of X-rays which have passed through the tested tissue; (b) measuring the values d.sub.k (3) (k(3) is a natural number, k(3)=1, 2, . . . , m/2) of X-ray density on said first X-ray projectional distribution Dl.sub.3 at m/2 (m is a natural number) positions spaced apart from each other from one end of said first X-ray projectional distribution D.sub.3 toward the other end thereof, and at the same time measuring the values d.sub.k (4) (k(4) is a natural number, k(4)=1, 2, . . . , m/2) of X-ray density on said second X-ray projectional distribution D.sub.4 at m/2 positions spaced apart from each other from one end of said second X-ray projectional distribution D.sub.4 toward the other end thereof, where said m/2 positions spaced apart from each other on the first and second X-ray projectional distributions D.sub.3, D.sub.4 for measurement of the values d.sub.k (3) and d.sub.k (4) of X-ray density are selected according to the following three criteria, (i) that the tomographic plane of the tested tissue of a body to be reconstructed is expressed by a pseudo-tomographic plane which is constituted collectively by mn pieces of square picture elements, with m pieces of picture elements in a row and n in a column (both m and n are natural numbers), which are formed by dividing said tomographic plane of the tested tissue of a body into small sections and each of which has a single piece of X-ray density information, and that said pseudo-tomographic plane is placed between an X-ray source and said two X-ray projectional distributions D.sub.3, D.sub.4, (ii) that said pseudo-tomographic plane is divided into a first part of a plane and a second part of a plane which are constituted collectively by said picture elements with m/2 pieces in a row and n pieces in a column, respectively, (iii) that n rows, each of which is constituted by m pieces of picture elements are numbered in order 1, 2, . . . , n from the left and that said m pieces of picture elements in each row are numbered respectively 1, 2, . . . , m; m+1, m+2 , . . . , 2 m; . . . ; (n-1)m+1, (n-1)m+2, . . . mn from the side of said X-ray source toward the side of said two X-ray projectional distributions D.sub.3, D.sub.4 in order that mn X-ray beams passing through said pseudo-tomographic plane from two directions comprise the first group of X-ray beams which is constituted by mn/2 X-ray beams in a direction of .theta..sub.3, passing through respectively the left lower corner of each picture element in said first part of a plane and the second group of X-ray beams which is constituted by mn/2 X-ray beams in a direction of .theta..sub.4 passing through respectively the left upper corner of each picture element in said second part of a plane, and said m/2 positions spaced apart from each other on said two X-ray projectional distributions D.sub.3, D.sub.4 for measurement of the values d.sub.k (3) and d.sub.k (4) of X-ray density correspond to the positions on said two X-ray projectional distributions D.sub.3, D.sub.4 which have X-ray density information to be obtained by passing first m/2 X-ray beams through said pseudo-tomographic plane based on the above-mentioned criteria, .theta..sub.3 indicates the angle at which each X-ray beam of the first group crosses with the base of each picture element in the first part of a plane, and .theta..sub.3 =tan.sup.-1 m and .theta..sub.4 indicates the angle at which each X-ray beam of the second group crosses with the base of each picture element in the second part of a plane, and .theta..sub.4 =-tan.sup.-1 m; (c) calculating X-ray absorption coefficient .mu..sub.t (t is a natural number, t=1, 2, . . . , m/2) of each of m/2 pieces of picture elements in the first part of a plane in accordance with the following equations based on the values d.sub.k (3) of X-ray density measured in step (b) and length of the X-ray beam in the direction of .theta..sub.3 passing through each picture element in the first part of a plane, and at the same time calculating X-ray absorption coefficient .mu..sub.t (t is a natural number, t=m/2+1, m/2+2, . . . , m) of each of m/2 pieces of picture elements in the second part of a plane in accordance with the following equations based on the values d.sub.k (4) of X-ray density measured in step (b) and length of the X-ray beams in the direction of .theta..sub.4 passing through each picture element in the second part of plane, ##EQU45## L is a square matrix of dimension m.times.m, T indicates a matrix transpose and .alpha. is a length of an X-ray beam passing through each picture element from directions of .theta..sub.3, .theta..sub.4 ; (d) memorizing X-ray absorption coefficients .mu..sub.1 .about..mu.m calculated in step (c); (e) measuring each of the values d.sub.k (3) (k(3) is a natural number, k(3)=m/2+1, m/2+2, . . . , m) of X-ray density on said first X-ray projectional distribution d.sub.3 at the positions numbering m/2 spaced apart from each other from the (m/2+1)position from one end of said first X-ray projectional distribution D.sub.3 toward the other end thereof, and at the same time measuring each of the values d.sub.k (4) (k(4) is a natural number, k(4)=m/2+1, m/2+2, . . . , m) of X-ray density on said second X-ray projectional distribution D.sub.4 at the positions numbering m/2 spaced apart from each other from the (m/2+1) position from D.sub.4 toward the other end thereof, where said positions numbering m/2 spaced apart from each other on said first X-ray projectional distribution D.sub.3 for measurement of the values d.sub.k (3) (k(3)=m/2+1, m/2+2, . . . , m) of X-ray density are selected such that said positions numbering m/2 spaced apart from each other on said first X-ray projectional distribution D.sub.3 for measurement of the values d.sub.k (3) (k(3)=m/2+1, m/2+2, . . . , m) of X-ray density correspond to the positions on said first X-ray projectional distribution D.sub.3 which have X-ray density information obtained as a result of the m/2 X-ray beams passing through the left lower corner of each of the respective picture elements numbered (m+1) to 3 m/2 passing through said first part of a plane based on the three criteria in step (b), and said positions numbering m/2 spaced apart from each other on said second X-ray projectional distribution D.sub.4 for measurement of the values d.sub.k (4) (k(4)=m/2+1, m/2+2, . . . , m) of X-ray density are selected such that said positions numbering m/2 spaced apart from each other on said second X-ray projectional distribution D.sub.4 for measurement of the values d.sub.k (4) (k(4)=m/2+1, m/2+2, . . . , m) of X-ray density correspond to the positions on said second X-ray projectional distribution D.sub.2 which have X-ray density information obtained as a result of the m/2 X-ray beams passing through the left upper corner of each of the respective picture elements numbered (3m/2+1) to 2 m passing through said second part of a plane based on the three criteria in step (b); (f) calculating the X-ray absorption coefficients .mu..sub.m+1 .about..mu..sub.3m/2 based on the X-ray absorption coefficients .mu..sub.1 .about..mu..sub.m calculated in step (c), the valuess d.sub.k (3) (k(3)=m/2+1, m/2+2, . . . , m) of X-ray density measured in step (e), and the length of X-ray beams passing through the picture elements numbered (m+1) to 3 m/2 from the .theta..sub.3 direction, and at the same time, calculating the X-ray absorption coefficients .mu..sub.3m/2+1 18 .mu..sub.2m based on the X-ray absorption coefficients .mu..sub.1 .about..mu..sub.m calculated in step (c), the values d.sub.k (4) (k(4)=m/2+1, m/2+2, . . . , m) of X-ray density measured in step (e), and the length of X-ray beams passing through the picture elements numbered (3m/2+1) to 2 m from the .theta..sub.4 direction, where the method of calculating the X-ray absorption coefficients .mu..sub.m+ 1.about..mu..sub.2m is the same as in step (c) and the X-ray absorption coefficients .mu..sub.1 .about..mu..sub.m calculated in step (c) are selectively used; (g) memorizing the X-ray absorption coefficients .mu..sub.m+1 .about..mu..sub.2m calculated in step (f); (h) calculating the X-ray absorption coefficient .mu..sub.2m+ 1.about..mu..sub.3m, .mu..sub.3m+ 1.about..mu..sub.4m, . . . , .mu.(n-1)m+1.about..mu..sub.mn repeating substantially the same steps as steps (e), (f) and (g) and memorizing them; (i) reconstructing the computed tomographic image of said tested tissue of a body based on the X-ray absorption coefficients .mu..sub.1 .about..mu..sub.m, .mu..sub.m+1 .about..mu..sub.2m , . . . , .mu..sub.(n-1) m+1 .about..sub.mn memorized in steps (d), (g) and (h), where the picture elements having respective X-ray absorption coefficients .mu..sub.1, .mu..sub.2, . . . , .mu..sub.mn calculated in step (c), (f) and (h) are positioned at the locations of said picture elements numbered 1, 2, . . . , mn of the pseudo-tomographic plane and wherein the complete collection of picture elements located in the m.times.n array constitute the reconstructed computed tomographic plane of the tested tissue of a body.

8. A reconstruction method of a computed tomographic image from a fiew X-ray projections comprising: (a) projecting X-rays from two symmetrical desired directions (.theta..sub.1, .theta..sub.2) toward tested tissue of a body for producing first and second X-ray projectional distributions D.sub.1, D.sub.2 of X-rays which have passed through the tested tissue; (b) measuring the values d.sub.k (1) (k(1) is a natural number) of X-ray density on said first X-ray projectional distribution D.sub.1 at at least ##EQU46## (m and n are natural numbers and the product of m and n is an even number) positions spaced apart from each other from one end of said first X-ray projectional distribution D.sub.1 toward the other end thereof, and at the same time measuring the values d.sub.k (2) (k(2) is a natural number) of X-ray density on said second X-ray projectional distribution D.sub.2 at at least ##EQU47## positions spaced apart from each other from one end of said second X-ray projectional distribution D.sub.2 toward the other end thereof, where each said ##EQU48## positions spaced apart from each other on the first and second X-ray projectional distributions D.sub.1, D.sub.2 for measurement of the values d.sub.k (1) and d.sub.k (2) are selected according to the three criteria, (i) that the tomographic plane of the tested tissue of a body to be reconstructed is expressed by a pseudo-tomographic plane which is constituted collectively by mn pieces of square picture elements, with m pieces of picture elements in a row and n in a column (both m and n are natural numbers), which are formed by dividing said tomographic plane of the tested tissue of body into small sections and each of which has a single piece of X-ray density information, and that said pseudo-tomographic plane is placed between an X-ray source and said two X-ray projectional distributions D.sub.1, D.sub.2, (ii) that said pseudo-tomographic plane is divided into a first part of a plane and a second part of a plane which are constituted collectively by said picture elements with m/2 pieces in a row and n pieces in a column, respectively, (iii) that n rows, each of which is constituted by m pieces of picture elements are numbered in order 1, 2, . . . , n from the left and that said m pieces of picture elements in each row are numbered respectively 1, 2, . . . , m; m+1, m+2, . . . , 2 m; . . . ; (n-1)m+1, (n-1 ) m+2, . . . mn from the side of said X-ray source toward the side of said two X-ray projectional distributions D.sub.1, D.sub.2 in order and that at least m(n+1) X-ray beams passing through said pseudo-tomographic plane from two directions (.theta..sub.1, .theta..sub.2) are constituted by the first group of X-ray beams in a direction of .theta..sub.1 and the second group of X-ray beams in a direction of .theta..sub.2, wherein the first group of X-ray beams comprise mn/2 X-ray beams, each of which passes through the left lower corner of one of the picture elements in the first part of the plane and at least m/2 X-ray beams passing through the picture elements in the n-th column in the first part of the plane, and the second group of X-ray beams comprises mn/2 X-ray beams, each of which passes through the left upper part of one of the picture elements in the second part of the plane and at least m/2 X-ray beams passing through the picture elements in the n-th column in the second part of the plane, said ##EQU49## positions spaced apart from each other on said two X-ray projectional distributions D.sub.1, D.sub.2 for measurement of the values d.sub.k (1) and d.sub.k (2) of X-ray density correspond to the positions on said two X-ray projectional distributions D.sub.1, D.sub.2 which have X-ray density information to be obtained by passing said X-ray beams through said pseudo-tomographic plane, .theta..sub.1 indicates the angle at which each X-ray beam of the first group crosses with the base of each picture element in the first part of a plane, and .theta..sub.1 =tan.sup.-1 m/2, and .theta..sub.2 indicates the angle at which each X-ray beam of the second group crosses with the base of each picture element in the second part of a plane, and .theta..sub.2 =-tan.sup.-1 m/2; (c) calculating X-ray absorption coefficient .mu..sub.t (t=1, 2, . . . , mn and t is a natural number) of each of mn pieces of picture elements in accordance with the following equations based on the X-ray density values d.sub.k (1) and d.sub.k (2) measured in step (b) and length of the X-ray beams passing through each of the picture elements, ##EQU50## L is a band matrix of dimension m(n+1).times.mn, T indicates a matrix transpose and .alpha. is a length of an X-ray beam passing through each picture element from directions of .theta..sub.1, and .theta..sub.2 ; (d) reconstructing the computed tomographic image of said tested tissue of a body where the picture elements having respective X-ray absorption coefficients .mu..sub.1, .mu..sub.2, . . . , .mu..sub.mn calculated in step (c) are positioned at the locations of said picture elements numbered 1, 2, . . . , mn of the pseudo-tomographic plane and wherein the completed collection of picture elements located in the m.times.n array constitute the reonstructed computed tomographic plane of the tested tissue of a body.

9. A reconstruction method of a computed tomographic image from a few X-ray projections comprising: (a) projecting X-rays from two symmetrical desired directions (.theta..sub.3, .theta..sub.4) toward tissue of a body for producing first and second X-ray projectional distributions D.sub.3, D.sub.4 of X-rays which have passed through the tested tissue; (b) measuring the values d.sub.k (3) (k(3) is a natural number) of X-ray density on said first X-ray projectional distribution D.sub.3 at at least ##EQU51## (m and n are natural numbers and the product of m and n is an even number) positions spaced apart from each other from one end of said first X-ray projectional distribution D.sub.1 toward the other end thereof, and at the same time measuring the values d.sub.k (4) (k(4) is a natural number) of X-ray density on said second X-ray projectional distribution D.sub.4 at at least ##EQU52## positions spaced apart from each other from one end of said second X-ray projectional distribution D.sub.4 toward the other end thereof, where each said ##EQU53## positions spaced apart from each other on the first and second X-ray projectional distributions d.sub.3, D.sub.4 for measurement of the values d.sub.k (3) and d.sub.k (4) of X-ray density are selected according to the following three criteria, (i) that the tomographic plane of the tested tissue of a body to be reconstructed is expressed by a pseudo-tomographic plane which is constituted collectively by mn pieces of square picture elements, with m pieces of picture elements in a row and n in a column (both m and n are natural numbers), which are formed by dividing said tomographic plane of the tested tissue of a body into small sections and each of which has a single piece of X-ray density information, and that said pseudo-tomographic plane is placed between an X-ray source and said two X-ray projectional distributions D.sub.3, D.sub.4, (ii) that said pseudo-tomographic plane is divided into a first part of a plane and a second part of a plane which are constituted collectively by said picture elements with m/2 pieces in a row and n pieces in a column, respectively, (iii) that n rows, each of which is constituted by m pieces of picture elements are numbered in order 1, 2, . . . , n from the left and that said m pieces of picture elements in each row are numbered respectively 1, 2, . . . , m; m+1, m+2, . . . , 2 m; . . . ; (n-b 1)m-1, (n-1)m+2, . . . mn from the side of said X-ray source toward the side of said two X-ray projectional distributions D.sub.3, D.sub.4 in order and that at least m(n+1) X-ray beams passing through said pseudo-tomographic plane from two directions (.theta..sub.3, .theta..sub.4) are constituted by the first group of X-ray beams in a direction of .theta..sub.3 and the second group of X-ray beams in a direction of .theta..sub.4, wherein the first group of X-ray beams comprises mn/2 X-ray beams, each of which passes through the left lower corner of one of the picture elements in the first part of a plane and at least m/2 X-ray beams passing through the picture elements in the n-th column in the first part of a plane, and the second group of X-ray beams comprises mn/2 X-ray beams, each of which passes through the left upper part of one of the picture elements in the second part of a plane and at least m/2 X-ray beams passing through the picture elements in the n-th column in the second part of a plane, said ##EQU54## positions spaced apart from each other on said two X-ray projectional distributions D.sub.3, D.sub.4 for measurement of the values d.sub.k (3) and d.sub.k (4) of X-ray density correspond to the positions on said two X-ray projectional distributions D.sub.3, D.sub.4 which have X-ray density information to be obtained by passing said X-ray beams through said pseudo-tomographic plane, .theta..sub.3 indicates the angle at which each X-ray beam of the first group crosses with the base of each picture element in the first part of a plane, and .theta..sub.3 =tan.sup.-1 m, and .theta..sub.4 indicates the angle at which each X-ray beam of the second group crosses with the base of each picture element in the second part of a plane, and .theta..sub.4 =-tan.sup.-1 m; (c) calculating X-ray absorption coefficient .mu..sub.t (t=1, 2, . . . , mn and t is a natural number) of each of mn pieces of picture elements in accordance with the following equations based on the X-ray density values d.sub.k (3) and d.sub.k (4) measured in step (b) and length of the X-ray beams passing through each of the picture elements, ##EQU55## L is a band matrix of dimension m(n+1).times.mn, T indicates the transpose of a matrix and .alpha. is a length of an X-ray beam passing through each picture element from directions of .theta..sub.3, .theta..sub.4 ; (d) reconstructing the computed tomographic image of said tested tissue of a body, where the picture elements having respective X-ray absorption coefficients .mu..sub.1, .mu..sub.2, . . . , .mu..sub.mn calculated in step (c) are positioned at the locations of said picture elements numbered 1, 2, . . . , mn of the pseudo-tomographic plane and wherein the complete collection of picture elements located in the m.times.n array constitute the reconstructed computed tomographic plane of the tested tissue of body.

10. A reconstruction method of a computed tomographic image from a few X-ray projections comprising: (a) projecting X-rays from two symmetrical desired directions (.theta..sub.1, .theta..sub.2) toward tested tissue of a body for producing first and second X-ray projectional distributions D.sub.1, D.sub.2 of X-rays which have passed through the tested tissue; (b) measuring the values d.sub.k (1) (k(1) is a natural number, k(1)=1, 2, . . . , m) of X-ray density on said first X-ray projectional distribution D.sub.1 at m (m is a natural number) positions spaced apart from each other from one end of said first projectional X-ray distribution D.sub.1 toward the other end thereof, and at the same time measuring the values d.sub.k (2) (k(2) is a natural number, k(2)=1, 2, . . . , m) of X-ray density on said second projectional X-ray distribution D.sub.2 at m positions spaced apart from each other from one end of said second projectional X-ray distribution D.sub.2 toward the other end thereof, where said m positions spaced apart from each other on the first and second X-ray projectional distributions D.sub.1, D.sub.2 for measurement of the values d.sub.k (1) and d.sub.k (2) of X-ray density are selected according to the following three criteria: (i) that the tomographic plane of the tested tissue of a body to be reconstructed is expressed by a pseudo-tomographic plane which is constituted collectively by mn pieces of square picture elements, with m pieces of picture elements in a row and n in a column (both m and n are natural numbers), which are formed by dividing said tomographic plane of the tested tissue of a body into small sections and each of which has a single piece of X-ray density information, and that said pseudo-tomographic plane is placed between an X-ray source and said two X-ray projectional distributions D.sub.1, D.sub.2, (ii) that said pseudo-tomographic plane is divided into a first part of a plane and a second part of a plane which are constituted collectively by said picture elements with m/2 pieces in a row and n pieces in a columnc, respectively, (iii) that n rows, each of which is constituted by m pieces of picture elements are numbered in order 1, 2, . . . ,n from the left and that said m pieces of picture elements in each row are numbered respectively 1,2, . . . ,m; m+1, m+2, . . . , 2m; . . . ; (n-1)m+1, (n-1)m+2, . . .mn from the side of said X-ray source toward the side of said two X-ray projectional distributions D.sub.1, D.sub.2 in order and that at least m(n+1) X-ray beams passing through said pseudo-tomographic plane from two directions (.theta..sub.1, .theta..sub.2) are divided into the first group of X-ray beams in a direction of .theta..sub.1 and the second group of X-ray beams in a direction of .theta..sub.2, where the first group of X-ray beams is constituted by mn/2 X-ray beams passing through respectively the left lower corner of each picture element in said first part of a plane and at least m/2 X-ray beams passing through the picture elements in the n-th column in the first part of a plane, and the second group of X-ray beams is constituted by mn/2 X-ray beams passing through respectively the left upper corner of each picture element in said second part of a plane and at least m/2 X-ray beams passing through the picture elements in the n-th column in the second part of a plane, and said m positions spaced apart from each other on said two X-ray projectional distributions D.sub.1, D.sub.2 for measurement of the values d.sub.k (1) and d.sub.k (2) of X-ray density correspond to the positions on said two X-ray projectional distribution D.sub.1, D.sub.2 which have X-ray density information to be obtained by passing first m X-ray beams through said pseudo-tomographic plane based on the above-mentioned criteria, .theta..sub.1 indicates the angle at which each X-ray beam of the first group crosses with the base of each picture element in the first part of a plane, and .theta..sub.1 = tan.sup.-1m/ 2, and .theta..sub.2 indicates the angle at which each X-ray beam of the second group crosses with the base of each picture element in the second part of a plane, and .theta..sub.2 = -tan.sup.-1m/ 2; (c) calculating the X-ray absorption coefficients .mu..sub.1.about. .mu..sub.2m of m picture elements in the first part of a plane and m picture elements in the second part of a plane comprising the picture elements in the first and second columns of the pseudo-tomographic plane, in accordance with the following equations based on the values d.sub.k (1), d.sub.k (2) of X-ray density measured in step (b) and the length of the X-ray beams passing through each picture element in the first and second parts of a plane, ##EQU56## L is a square matrix of dimension 2m.times.2m, T indicates a matrix transpose and .alpha. is a length of an X-ray beam passing through each picture element from directions of .theta..sub.1, .theta..sub.2 ; (d) memorizing the X-ray absorption coefficients .mu..sub.1 .about..mu..sub.m which are the first m of the X-ray absorption coefficients .mu..sub.1 .about..mu..sub.2m calculated in step (c); (e) measuring each of the values d.sub.k (1) and d.sub.k (2) (k(1), k(2)=m/2+1, m/2+2,...,3m/2) of X-ray density on the first and second X-ray projectional distributions D.sub.1 and D.sub.2 respectively at the positions numbering m spaced apart from each other from the ##EQU57## position from one end of said first and second X-ray projectional distributions D.sub.1, D.sub.2 toward the other end thereof, where said positions numbering m spaced apart from each other on each of said first X-ray projectional distribution D.sub.1 and said second X-ray projectional distribution D.sub.2 for measurement of the values d.sub.k (1), d.sub.k (2) (k(1), k(2)=m/2+1, m/2+2, . . . , 3m/2) of X-ray density are selected such that said positions numbering m spaced apart from each other on said first X-ray projectional distribution D.sub.1 for measurement of the values d.sub.k (1) (k(1)=m/2+1, m/2+2, . . . , 3m/2) of X-ray density correspond to the positions on said first X-ray projectional distribution D.sub.1 which have X-ray density information obtained as a result of the m X-ray beams passing through the left lower corner of each of the respective picture elements numbered (m+1) to 3m/2 and (2m+1) to 5m/2 passing through said first part of a plane based on the three assumptions in step (b), and said positions numbering m spaced apart from each other on said second X-ray projectional distribution D.sub.2 for measurement of the values d.sub.k (2) (k(2)=m/2+1, m/2+2, . . . , 3m/2) of X-ray density are selected such that said positions numbering m spaced apart from each other on said second X-ray projectional distribution D.sub.2 for measurement of the values d.sub.k (2) (k(2)=m/2+1, m/2+2, . . . , 3m/2) of X-ray density correspond to the positions on said second X-ray projectional distribution D.sub.2 which have X-ray density information obtained as a result of the m X-ray beams passing through the left upper corner of each of the respective picture elements numbered ##EQU58## to 2m and ##EQU59## .about.3m passing through said second part of a plane based on the three criteria in step (b); (f) calculating the X-ray absorption coefficients .mu..sub.m+1 .about..mu..sub.3m/2 and .mu..sub.2m+1 .about..mu.5m/2 based on the X-ray absorption coefficients .mu..sub.1 .about..mu..sub.2m calculated in step (c), the values d.sub.k (1) (k(1)=m/2+1, m/2+2, . . . , 3m/2) of X-ray density measured in step (e), and the length of X-ray beams passing through the picture elements numbered (m+1) to 3m/2 and (2m+1).about.5m/2 from the .theta..sub.1 direction, and at the same time, calculating the X-ray absorption coefficients .mu..sub.3m/2 +1.about..mu..sub.2m and .mu..sub.5m/2 .about..mu..sub.3m based on the X-ray absorption coefficients .mu..sub.1 .about..mu..sub.2m calculated in step (c), the values d.sub.k (2) (k(2)=m/2+1, m/2+2, . . . ,3m/2) of X-ray density measured in step (e), and the length of X-ray beams passing through the picture elements numbered ##EQU60## to 2m and ##EQU61## to 3m from the .theta..sub.2 direction, where the method of calculating the X-ray absorption coefficients .mu..sub.m+1 .about..mu..sub.3m is the same as in ste (c) and the X-ray absorption coefficients .mu..sub.1 .about..mu..sub.2m calculated in step (c) are selectively used; (g) memorizing the X-ray absorption coefficients .mu..sub.m+1 .about..mu..sub.2m, comprising the first m of the X-ray absorption coefficients .mu..sub.m+1 .about..mu..sub.3m calculated in step (f); (h) calculating the X-ray absorption coefficient .mu..sub.2m+1 .about..mu..sub.4m, .mu..sub.3m+1 .about..mu..sub.5m, . . . ,.mu..sub.(n-1)m+1 .about..mu..sub.(n+1)m repeating substantially the same steps as steps (e), (f) and (g) and memorizing the first m of the X-ray absorption coefficients .mu..sub.2m+1 .about..mu..sub.3m, .mu..sub.3m+1 .about..mu..sub.4m, . . . , .mu..sub.(n-1)m+1 .about..mu..sub.mn; (i) reconstructing the computed tomographic image of said tested tissue of a body based on the X-ray absorption coefficients .mu..sub.1 .about..mu..sub.m, .mu..sub.m+1 .about..mu..sub.2m, . . . , .mu..sub.(n-1)m+1 .about..mu..sub.mn memorized in steps (d), (g) and (h), where the picture elements having respective X-ray absorption coefficients .mu..sub.1, .mu..sub.2, . . . , .mu..sub.mn memorized in steps (d), (g) and (h) are positioned at the locations of said picture elements numbered 1, 2, . . . , mn of the pseudo-tomographic plane and wherein the complete collection of picture elements located in the m.times.n array constitute the reconstructed computed tomographic plane of the tested tissue of body.

11. A reconstruction method of a computed tomographic image from a few X-ray projections comprising: (a) projecting X-rays from two symmetrical desired directions (.theta..sub.3, .theta..sub.4) toward tested tissue of a body for producing first and second X-ray projectional distributions D.sub.3, D.sub.4 of X-rays which have passed through the tested tissue; (b) measuring the values d.sub.k (3) (k(3) is a natural number, k(3)=1, 2, . . . , m) of X-ray density on said first X-ray projectional distribution D.sub.3 Heach other from one end of said second X-ray projectional distribution D.sub.4 toward the other end thereof, where said m positions spaced apart from each other on the first and second X-ray projectional distributions D.sub.3, D.sub.4 for measurement of the values d.sub.k (3) and d.sub.k (4) of X-ray density are selected according to the following three criteria, (i) that the tomographic plane of the tested tissue of a body to be reconstructed is expressed by a pseudo-tomographic plane which is constituted collectively by mn pieces of square picture elements, with m pieces of picture elements in a row and n in a column (both m and n are natural numbers), which are formed by dividing said tomographic plane of the tested tissue of a body into small sections and each of which has a single piece of X-ray density information, and that said pseudo-tomographic plane is placed between an X-ray source and said two X-ray projectional distributions D.sub.3, D.sub.4, (ii) that said pseudo-tomographic plane is divided into a first part of a plane and a second part of a plane which are constituted collectively by said picture elements with m/2 pieces in a row and n pieces in a column, respectively, (iii) that n rows, each of which is constituted by m pieces of picture elements are numbered in order 1, 2,..., n from the left and that said m pieces of picture elements in each row are numbered respectively 1, 2, . . . , m; m+1, m+2, . . . , 2m; . . .; (n-1)m+1, (n-1)m+2, . . .mn from the side of said X-ray source toward the side of said two X-ray projectional distributions D.sub.3, D.sub.4 in order and that at least m(n+1) X-ray beams passing through said pseudo-tomographic plane from two directions (.theta..sub.3, .theta..sub.4) are divided into the first group of X-ray beams in a direction of .theta..sub.3 and the second group of X-ray beams in a direction of .theta..sub.4, wherein the first group of X-ray beams is constituted by mn/2 X-ray beams passing through respectively the left lower corner of each picture element in said first part of the plane and at least m/2 X-ray beams passing through the picture elements in the n-th column in the first part of the plane, and the second group of X-ray beams is constituted by mn/2 X-ray beams passing through respectively the left upper corner of each picture element in said second part of the plane at at least m/2 X-ray beams passing through the picture elements in the n-th column in the second part of the plane, said m positions spaced apart from each other on said two X-ray projectional distributions D.sub.3, D.sub.4 for measurement of the values d.sub.k (3) and d.sub.k (4) of X-ray density correspond to the positions on said two X-ray projectional distributions D.sub.3, D.sub.4 which have X-ray density information to be obtained by passing the first m X-ray beams through said pseudo-tomographic plane based on the above-mentioned criteria, .theta..sub.3 indicates the angle at which each X-ray beam of the first group crosses with the base of each picture element in the first part of a plane, and .theta..sub.3 = tan.sup.-1 m, and .theta..sub.4 indicates the angle at which each X-ray beam of the second group crosses with the base of each picture element in the second part of a plane, and .theta..sub.4 = tan.sup.-1 m; (c) calculating the X-ray absorption coefficients .mu.1.about..mu..sub.2m of m picture elements in the first part of a plane and m picture elements in the second part of a plane comprising the picture elements in the first and second columns of the pseudo-tomographic plane, in accordance with the following equations based on the values d.sub.k (3), d.sub.k (4) of X-ray density measured in step (b) and the length of the X-ray beams passing through each picture element in the first and second parts of a plane, ##EQU62## L is a square matrix of dimension 2m.times.2m, T indicates a matrix transpose and .alpha. is a length of the X-ray beam passing through each picture element from directions of .theta..sub.3, .theta..sub.4 ; (d) memorizing the X-ray absorption coefficients .mu..sub.1 .about..mu..sub.m comprising the first m of the X-ray absorption coefficients .mu..sub.1 .about..mu..sub.2m calculated in step (c); (e) measuring each of the values d.sub.k (3) and d.sub.k (4) (k(3), k(4)=m/2+1, m/2+2,..., 3m/2) of X-ray density on the first and second X-ray projectional distributions D.sub.3 and D.sub.4 respectively at the positions numbering m spaced apart from each other from the ##EQU63## position from one end of said first and second X-ray projectional distributions D.sub.3, D.sub.4 toward the other end thereof, where said positions numbering m spaced apart from each other on each of said first X-ray projectional distribution D.sub.3 and said second X-ray projectional distribution D.sub.4 for measurement of the values d.sub.k (3), d.sub.k (4) (k(3), d(4)=m/2+1, m/2+2, . . . , 3m/2) of X-ray density are selected such that said positions numbering m spaced apart from each other on said first X-ray projectional distribution D.sub.3 for measurement of the values d.sub.k (3) (k(3)=m/2+1, m/2+2, . . . , 3m/2) of X-ray density correspond to the positions on said first X-ray projectional distribution D.sub.3 which have X-ray density information obtained as a result of the m X-ray beams passing through the left lower corner of each of the respective picture elements numbered (m+1) to 3m/2 and (2m+1) to 5m/2 passing through said first part of a plane based on the three assumptions in step (b), and said positions numbering m spaced apart from each other on said second X-ray projectional distribution D.sub.4 for measurement of the values d.sub.k (4) (k(4)=m/2+1, m/2+2, . . . ,3m/2) of X-ray density are selected such that said positions numbering m spaced apart from each other on said second X-ray projectional distribution D.sub.4 for measurement of the values d.sub.k (4) (k(4)=m/2+1, m/2+2, . . . , 3m/2) of X-ray density correspond to the positions on said second X-ray projectional distribution D.sub.4 which have X-ray density information obtained as a result of the m X-ray beams passing through the left upper corner of each of the respective picture elements numbered ##EQU64## to 2m and ##EQU65## .about.3m passing through said second part of a plane based on the three assumptions in step (b); (f) calculating the X-ray absorption coefficients .mu..sub.m+ 1.about..mu..sub. 3m/2 and .mu..sub. 2m+1.about..mu..sub. 5m/2 based on the X-ray absorption coefficients .mu..sub.1 .about..mu..sub.2m calculated in step (c), the values d.sub.k (3) (k(3)=m/2+1, m/2+2, . . . , 3m/2) of X-ray density measured in step (e), and the length of X-ray beams passing through the picture elements numbered (m+1) to 3m/2 and (2m+1).about.5m/2 from the .theta..sub.3 direction, and at the same time, calculating the X-ray absorption coefficients .mu..sub.3m/2 +1.about..mu..sub.2m and .mu..sub.5m/2 .about..mu..sub.3m based on the X-ray absorption coefficients .mu..sub.1 .about..mu..sub.2m calculated in step (c), the values d.sub.k (4) (k(4)=m/2+1, m/2+2,...., 3m/2) of X-ray density measured in step (e), and the length of X-ray beams passing through the picture elements numbered ##EQU66## to 2m and ##EQU67## to 3m from the .theta..sub.4 direction, where the method of calculating the X-ray absorption coefficients .mu..sub.m+1 .about..mu..sub.3m is the same as in step (c) and the X-ray absorption coefficients .mu..sub.1 .about..mu..sub.2m calculated in step (c) are selectively used; (g) memorizing the X-ray absorption coefficients .mu..sub.m+1.about..mu..sub.2m comprising the first m of the X-ray absorption coefficients .mu..sub.m+1.about..mu..sub.3m calculated in step (f); (h) calculating the X-ray absorption coefficient .mu..sub.2m+1 .about..mu..sub.4m, .mu..sub.3m+1 .about..mu..sub.5m,....., .mu..sub.(n-1)m+1 .about..mu..sub.(n+1)m repeating substantially the same steps (e), (f) and (g) and memorizing the first m of the X-ray absorption coefficients .mu..sub.2m+1 .about..mu..sub.3m, .mu..sub.3m+1 .about..mu..sub.4m, . . . , .mu..sub.(n-1)m+1 .about..mu..sub.mn ; (i) reconstructing the computed tomographic image of said tested tissue of a body based on the X-ray absorption coefficients .mu..sub.1 .about..mu..sub.m, .mu..sub.m+1 .about..mu..sub.2m, . . . , .mu..sub.(n-1)m+1 .about..mu..sub.mn memorized in steps (f), (g) and (h), where the picture elements having respective X-ray absorption coefficients .mu..sub.1, .mu..sub.2. . . , .mu..sub.mn memorized in steps (f), (g) and (h) are positioned at the locations of said picture elements number 1, 2, . . . , mn of the pseudo-tomographic plane and wherein the complete collection of picture elements located in the m.times.n array constitute the reconstructed compouted tomographic plane of the tested tissue of a body.