Systems and method for generating an image

[0001] The present application claims priority from U.S. Provisional Patent Application No. 60/370,521, entitled “System and Process for Previously-Obtained 2-Dimensional or 3-Dimensional Spatial Information for Diffuse Optical Imaging,” filed Apr. 5, 2002, the entire disclosure of which is incorporated herein by reference in its entirety.

[0002] The invention was made with the U.S. Government support under Grant No. DAMD17-99-2-9001 awarded by the U.S. Department of the Army. Thus, the U.S. Government has certain rights in the invention.

[0003] The present invention relates generally to a system and method for generating an image. In particular, the present invention is directed to a system and method in which first and second images of a subject or a portion of the subject are obtained (e.g., simultaneously or sequentially), and the first image is reconstructed based on the second image to generate a resultant image having a spatial resolution which is greater than a spatial resolution of the first image.

[0004] The development of Diffuse Optical Tomography (“DOT”) for obtaining three-dimensional images of spatially varying absorption and scattering properties of a highly scattered media probed by near infrared light has been rapidly advancing. The clinical application of the DOT techniques to imaging breast cancer and brain pathology has shown increased promise. This is the case along with the appearance of preliminary results indicating the feasibility of extracting physiologically relevant information from the images reconstructed from the diffuse optical measurements. Because the inverse imaging problem for the DOT is ill-conditioned and generally under-determined, the image quality may likely suffer from poor spatial resolution and a sensitivity to measurement noise. This image quality can be improved by optimizing the geometry and the number of measurements being performed. However, significant improvements using such techniques may likely be obtained only by including previously-obtained information into the image reconstruction.

[0005] The use of a hard structural constraint provided by Magnetic Resonance Imaging (“MRI”) and Ultrasound Imaging (“UI”) techniques to reconstruct the optical diffuse image is known. In these conventional approaches, three-dimensional spatial information for different structures within the highly scattered medium are identified by the MRI or UI techniques, and a previously obtained optical diffuse image is reconstructed based on the MRI/UI image to obtain a resultant image. Specifically, it can be assumed that the boundaries of the structures identified by the MRI/UI technique also serve as the boundaries for piece-wise continuous structures within the diffuse optical image. Given these hard structural constraints, the DOT problem is then reduced to characterizing the optical properties within the specified target structures. Nevertheless, because the correlation between an MRI/UI contrast and a DOT contrast has not been explored, the validity of the assumption in the hard constraint has remained unclear.

[0006] Therefore, a need has arisen to provide a system and method for generating an image which overcome the above-described and other shortcomings of the related art.

[0007] According to an exemplary embodiment of the present invention, a system and method for generating the resultant image are provided. Specifically, each of a first image (e.g., an optical diffuse image) and a second image (e.g., an X-ray image, a magnetic resonance image, a functional magnetic resonance image, a computed tomography image, an ultrasound image, etc.) of a subject (e.g., a human, an animal, etc.) or a portion of the subject is obtained. For example, the first and the second images may be simultaneously or sequentially obtained. The first image includes a first portion of the subject and a second portion of the subject. Moreover, the second image is used to determine a first probability indicating that the first portion has a contrast which is greater than or equal to a predetermined contrast (e.g., a contrast associated with an abnormality within the subject, such as a tumor, a lesion, etc.). The second image is also used to determine a second probability indicating that the second portion has a contrast which is greater than or equal to the predetermined contrast, and the second probability is greater than the first probability, i.e., it is more likely that the second portion of the first image includes the abnormality. For example, the first probability may be about 0% and the second probability may be about 100%. Moreover, the first and second probabilities are used to reconstruct the first image, thereby generating the resultant image. Specifically, the first portion is reconstructed based on the first probability to generate a reconstructed first portion of the resultant image, and the second portion is reconstructed based on the second probability to generate a reconstructed second portion of the resultant image. Moreover, the system and method may reconstruct the first image based on the first probability and the second probability to generate the resultant image, thus increasing spatial resolution of the resultant image relative to the spatial resolution of the conventional resultant image. In this manner, spatial information from the second image may be used as a soft constraint on the first image to generate the resultant image.

[0008] In a variant of this embodiment of the present invention, the first image can also include a third portion of the subject (e.g., the third portion can separate the first portion from the second portion). For example, the third portion can be an outer edge of the abnormality within the subject, and may be subdivided into a plurality of third portions. In this exemplary variant, the second image can also be used to determine a third probability indicating that the third portion has a contrast which is greater than or equal to the predetermined contrast. For example, the third probability may be less than the second probability and greater than the first probability. In another exemplary embodiment, the third portion can be subdivided into a plurality of third portions, and each of the third portions may have a different third probability. In addition, each of the third probabilities may be less than the second probability and greater than the first probability, and may be used to blur the outer edges of the abnormality in the resultant image.

[0009] For example, when a distance between a particular point within the first image and a center of the abnormality is less than or equal to a first predetermined distance, the probability that the particular point includes the abnormality may be 100%. In a further exemplary embodiment, the second portion of the first image may include all or substantially all of these particular points, and the second probability may be 100%. When the distance between an intermediate point within the first image and the center of the abnormality is greater than the first predetermined distance but is less than or equal to a second predetermined distance, the probability that the particular point includes the abnormality may be greater than 0% but less than 100%.

[0010] In yet another exemplary embodiment of the present invention, the third portion of the first image may include all or substantially all of these intermediate points within the first image, and the third probability may be greater than 0% but less than 100%. For example, the third portion may include the outer edge of the abnormality, and the third probability associated with each of the intermediate points within the third portion may vary depending on the location of the intermediate point within the third portion. The intermediate points which are closest to the center of the abnormality may have an associated third probability equal to 100%−X %, where X is a percentage greater than 0% but less than 50%, and the intermediate points which are closest to the outer edge of the abnormality may have an associated third probability equal to 0%+X %. Moreover, the intermediate points which are positioned between the intermediate points closest to the center of the abnormality and the intermediate points closest to the outer edge may have an associated third probability which is greater than 0%+X % but less than 100%−X %, depending on their exact location within the third portion. When a distance between a further point within the first image and the center of the abnormality is greater than the first and second predetermined distances, the probability that the further point includes the abnormality may be 0%. In a variant of the exemplary embodiment of the present invention, the first portion of the first image may include all or substantially all of these further points, and the first probability may be 0%.

[0011] In still another exemplary embodiment of the present invention, one or more first regulation parameters associated with the first probability may be selected. For example, the first regulation parameter(s) may be associated with an optical absorption of the first portion of the first image, and/or an optical scattering of the first portion of the first image. Similarly, one or more second regulation parameters associated with the second probability may be selected. For example, the second regulation parameter(s) may be associated with an optical absorption of the second portion of the first image, and/or an optical scattering of the second portion of the first image.

[0012] In particular, the first regulation parameter(s) may control the reconstruction of the first portion, the second regulation parameter(s) can control the reconstruction of the second portion, and the second regulation parameter may be less than or equal to the first regulation parameter. For example, a normalized value of the first regulation parameter(s) may be between about 0.1 and about 1, and a normalized value of the second regulation parameter(s) can be greater than zero and less than or equal to about 0.1. The normalized value for the first regulation parameter(s) may be selected using a L-curve procedure. Moreover, after the normalized value for the first regulation parameter(s) is selected, the normalized value for the second regulation parameter(s) may be selected by balancing two inversely related factors. The first factor may be the resolution of the reconstructed second portion of the resultant image, and the second factor can be an amount of noise generated in the reconstructed second portion of the resultant image. For example, increasing the second regulation parameter(s) decreases the amount of noise generated in the reconstructed second portion, and also decreases the resolution of the reconstructed second portion. Similarly, decreasing the second regulation parameter(s) increases the resolution of the reconstructed second portion, and also increases the amount of noise generated in the reconstructed second portion. By balancing these two factors, an optimum normalized value for second regulation parameter(s) may be selected.

[0013] According to a particular exemplary embodiment of the present invention, another system and method for generating the resultant image are provided. For example, an optical diffuse image, a magnetic resonance image, and a functional magnetic resonance image of the subject or a portion of the subject is obtained. The first image includes a first portion of the subject and a second portion of the subject. Moreover, the second image and the third image are used to determine the first probability that the first portion has a contrast which is greater than or equal to the predetermined contrast. The second image and the third image are also used to determine the second probability that the second portion has a contrast which is greater than or equal to the predetermined contrast, and the second probability is greater than the first probability. Moreover, the first and second probabilities may be used to reconstruct the first image, thereby generating the resultant image. Specifically, the first portion can be reconstructed based on the first probability to generate the reconstructed first portion of the resultant image, and the second portion can be reconstructed based on the second probability to generate the reconstructed second portion of the resultant image.

[0014] In this exemplary embodiment, the first regulation parameter(s) associated with the first probability may be selected e.g., using the L-curve procedure. Similarly, the second regulation parameter(s) associated with the second probability may be selected, e.g., by balancing the two inversely related factors to select the optimum normalized value for the second regulation parameter(s). After the resultant image is generated, the resultant image then may be used to determine each of a rate of a flow of blood within the abnormality, a volume of the blood within the abnormality, and a deoxyhemoglobin concentration within the abnormality. Based on the information related to the flow of the blood, the volume of the blood, and the deoxyhemoglobin concentration within the abnormality, an amount of oxygen consumed by the abnormality may then be determined.

[0015] Other objects, features, and advantage will be apparent to persons of ordinary skill in the art from the following detailed description of the invention and the accompanying drawings.

[0044] Embodiments of the present invention and their features and advantages may be understood by referring to FIGS. 1-18, like numerals being used for like corresponding parts in the various drawings.

a. Theory

[0045] Generally, according to the present invention, each of a first image (e.g., an optical diffuse image) and a second image (e.g., an X-ray image, a magnetic resonance image, a functional magnetic resonance image, a computed tomography image, an ultrasound image, etc.) of a subject (e.g., a human, an animal, etc.) or a portion of the subject can be obtained, e.g., simultaneously or sequentially. Information included in the second image may then be used to provide soft constraints which are used to reconstruct the first image. In this example, the first image may be a three-dimensional diffuse optical image, and the second image can be a two-dimensional X-ray image. Moreover, the soft-constraints from the two-dimensional X-ray image can be incorporated into the Diffuse Optical Tomography (“DOT”) problem through the minimization of an objective function:
F(x)=(Φ_m−Φ_t(x))^T·(Φ_m−Φ_t(x))+λ_a(P_ax−γ)^T·(P_ax−γ)+λ_s(P_sx−γ)^T·(P_sx−γ).

[0046] This equation has the following exemplary terms: (a) the residual between an optical measurement and a theoretical estimate of the optical measurement, and (b) a difference between a projection of the three-dimensional diffuse optical absorption/scattering image and the two-dimensional X-ray image. The unknown “x” is a vector of an absorption coefficient μ_a′ and a reduced scattering coefficient μ_s′ at each voxel within the medium. Thus, the length of such “x” vector is identified as 2N_vox, where N_vox is the number of voxels within the medium to be imaged. The measurements of the diffuse photon fluence are defined by the vector Φ_m, where each element represents a measurement with a different source-detector pair. The theoretical estimate of the measured photon fluence is provided by Φ_t(x), e.g., a function of the optical properties within the medium. A pair of regularization parameters for controlling a correlation between the absorption (scattering) image and the X-ray image is given by λ_a (λ_s). The normalized two-dimensional X-ray image is given by the vector γ, such that the sum of all elements equals to one.

[0047] The projection of the three-dimensional absorption, and the reduced scattering onto the two-dimensional X-ray image can be handled by P_a and P_s, respectively, as defined herein. P_a is defined as the projection of the three-dimensional absorption image onto a two-dimensional image that is co-registered with the two-dimensional X-ray image, and P_s is defined as the projection of the three-dimensional scattering image onto the two-dimensional image that is co-registered with the two-dimensional X-ray image. These projection operators also normalize the result such that the sum of the elements of P_ax and the sum of the elements of P_sx equal to one. Such normalization allows the X-ray image to be used as a structural guide for the diffuse optical image, without placing any constraint on the magnitude of the diffuse optical image, without assuming a linearity between the X-ray and DOT contrast. By separating the constraint on the absorption and scattering, it is possible to tune the details of the correlation expected with the two-dimensional X-ray image. It should be understood that a soft structural constraint is being formulated on the three-dimensional diffuse optical image from a two-dimensional X-ray image, whereas the conventional systems and processes used hard three-dimensional structural constraints. The formulation presented in the equation above can be modified to handle a soft structural constraint from a three-dimensional image obtained from X-ray, magnetic resonance, functional magnetic resonance, computed tomography, ultrasound, etc.

[0048] For the case of fewer measurements than the unknowns, the linear problem is likely to be underdetermined, and can be defined by a regularized Moore-Penrose generalized inverse function:
Δx=B^T(BB^T+λ_tikI)⁻¹y,
where I is the identity matrix, and λ_tik is the Tikhonov regularization parameter. The matrix B can be defined as:
B=[A(λ_aP_a)(λ_aP_a)]^T,
where the matrix A is the linear transformation relating the change in the optical properties of the medium represented by Δx to the change in the optical measurements, as known in the art.

[0049] The matrices P_a and P_s can sparse, and may project and normalize the three-dimensional diffuse optical absorption and scattering image, respectively, into a two-dimensional image in the plane of the X-ray image. Thus, each row of P_a and P_s preferably represents an X-ray pixel, and each column represents an absorption or scattering voxel. Thus, each such element is zero if the voxel is not projected into the pixel; otherwise it is 1/N_a or 1/N_s for P_a and P_s, respectively, where N_a (N_s) equals the sum of μ_a (μ_s′) over all voxels. For P_a, all scattering voxels are preferably not projected into the pixel, and therefore all of those columns can be equal to zero, which may be the case for P_s. The vector y contains the diffuse optical and X-ray measurements, e.g.,
y=[ηγ]^T,
where η_i=1n[Φ_m,i/Φ_o,i] and Φ_o,i is a background photon fluence that may be measured without any perturbation in the optical properties. Each element of γ can be the value of a pixel in the normalized X-ray image.

[0050] In a second example, a Born approximation of the diffusion equation as the forward model of light propagating through tissue, and a modified Tiknov regularization for the inverse problem may be used. In this example, the soft-constraint of x-ray image can be incorporated into the DOT problem through the minimization of a cost function φ:
φ=∥y−A·f∥²+α₁∥(I−S)·f∥²+α₂∥S·f∥²

[0051] Such cost function has three separate terms: (i) a residual between the optical measurement and the theoretical estimate of the measurement, (ii) a norm of the part of image that doesn't have a X-ray contrast, and (iii) a norm of the part of image that has a X-ray contrast. f is defined as the optical image to be reconstructed. A is defined as the weight matrix calculated using three-point Green function of the diffuse approximation. y is defined as the data set. I is defined as the identity matrix. S is a diagonal two-value matrix with x-ray contrast information, e.g., a binary matrix when the subject is divided into two portions or a normalized matrix when the subject is divided into three or more portions. The solution of the minimization of the cost function φ (is as follows:
f=y^T·A·[A^T·A+I·α({right arrow over (r)})]⁻¹
where α(r) is a spatially variant regularization parameter, which is allowed to vary spatially within the pixels of the image, (which has a two-value function). In particular, α₂ can be assigned a small value (e.g., less than about 0.1) so we can increase the interested area's contrast and resolution. FIG. 1 shows an exemplary representative illustration 10 of such spatially variant regulation parameter which can be used by exemplary embodiments of a system and method according to the present invention. When such increase takes place, the high frequency noise inside of the interested area may also increase. Therefore, as set forth in detail below, the spatial resolution of the reconstructed image may be compared to the amount of noise inside the interested area of the reconstructed image when selecting optimum regularization parameters.
b. Testing Theory Via Simulation

[0052] A transmission measurement can be simulated via a slab representative of a clinical breast measurement. In the exemplary simulation, sixteen optical sources and sixteen optical detectors spanning 6×6 cm can be used to image two lesions, one lesion with contrast in the absorption coefficient and the other with contrast in the scattering coefficient. Realistic noise may be added to the simulated measurements. The results of the image reconstruction in this example, without the use of the spatial constraint, is shown in FIG. 2A for the absorption image, and in FIG. 2B for the scattering image. As shown in these illustrations, the images are dominated by the image noise because the soft spatial constraint is not utilized. This image noise can significantly be reduced by applying the spatial constraint, thus allowing the two lesions to be more accurately characterized, as shown in FIG. 3A for the absorption image, and in FIG. 3B for the scattering image.

[0053] As shown in FIG. 4B, a forward model representing a homogeneous medium 20 can be generated for testing and implementation of the concepts of the second example. This generation step (i.e., step 110) is illustrated in a flow diagram of a first exemplary embodiment of the method of the present invention shown in FIG. 4A. In particular, an exemplary wave length of 780 μm, a modulation frequency of 200 megahertz can be selected. A background optical property can be set as follows: μ_a=0.05 cm⁻¹ and μ_s=5 cm⁻¹. A spherical heterogeneity with radius of 1 cm and the optical property of μ_a 0.1 cm⁻¹ can be placed in the center of the homogeneous medium. The Gaussian type of noise can also added to the data so that the signal to noise ratio may be approximately 20˜40 dB.

[0054] Thereafter, a reconstruction procedure can be performed on the image of the homogeneous medium using x-ray constraints to obtain improved images, as provided in step 120 of FIG. 4A. FIG. 5A shows the image providing the results of the reconstruction procedure of FIG. 4A which do not use the x-ray constraints. This exemplary image can be compared with the improved image results, as shown in FIG. 5B, in which the image was reconstructed using such x-ray constraints. Both of these drawings illustrate the images extending along the Z-direction of the homogeneous medium. In particular, FIG. 5A shows the image reconstructed without the above-referenced constraints in which α₁=α₂=0.7. In contrast, FIG. 5B shows the improved image that was reconstructed with such constraints, in which α₁=0.7 and α₂=0.04. As can be clearly seen in FIGS. 5A and 5B, the image of FIG. 5B has an improved resolution and contract in comparison with the image of FIG. 5A.

[0055] Then, during step 120 of the method shown in FIG. 4A, a Born approximation formulation can be inserted into the implementation and generation of the images. In particular, by utilizing such formulation, the additive noise that propagates to the reconstruction can be calculated using the equation minimization of the cost function φ described herein above. Using the Born approximation formulation, the “y” value in the equation minimization formula can be replaced by the noise standard deviation (“STD”) added into the data. The resultant modified image of such replacement of the “y” value is shown in FIG. 6. As illustrated in this modified image, the region thereof regularized by α₂ has a higher noise STD, thus indicating that these pixels are more sensitive to the high frequency noise.

[0056] It is also possible to introduce a number of values into this formulation to quantitatively examine the effect of regularization parameters α₂ on the quality of the reconstruction. For example, the following quantities can be introduced as described below:

• [0057] Contrast 1: the ratio of the mean of the object and noise STD outside the interested area, and
• [0058] Contrast 2: the ratio of the mean of the object and noise STD inside the interested area.

[0059] FIG. 7 shows a one-dimensional presentation of the two-dimensional image acquired by a line sampling along the X direction. The higher level curve 150 indicates the amplitude of the noise free signal (contrast), and the lower level curve 160 indicates the amplitude of noise. A relatively good image requires both high Contrast 1 (e.g., a ratio of the noise free signal inside the interested region to noise outside the interested region) and high Contrast 2 (e.g., a ratio of the noise free signal inside the interested region to noise inside the interested region). Changing the regularization parameters (α₁, α₂) can affect Contrast 1 and Contrast 2 differently, and an appropriate regularization may optimize Contrast 1 and Contrast 2 as a whole.

[0060] FIGS. 8A and 8B illustrate the exemplary relationship between such quantities, i.e., Contrast 1, Contrast 2 and α₂ (given α₁), respectively. As shown in these figures, Contrast 1 decreases monotonically as α₂ increases (see FIG. 8A), and Contrast 2 tends to increase as α₂ increases (see FIG. 8B). Although a smaller α₂ provides a higher Contrast 1, Contrast 2 is more likely to be contaminated by the noise inside the interested region (e.g., the X-ray region). According to the present invention, is preferable to select an optimized α₂ as a balance between these two competing factors. It is also preferable to determine α₁ prior to the determination of the optimized α₂. In particular, the entire region can be assigned to one parameter, e.g., α₁. In this example, an L-curve technique can be utilized, as shown in FIG. 11, and as shall be described in further detail below.

[0061] In addition to Contrast 1 and Contrast 2, another quantity which can be used to describe the quality of the image is the resolution of the image. In particular, FIGS. 9A and 9B illustrate graphs which indicate that the resolution of the images worsens as α₂ increases (e.g., the resolution changes at different regularization parameters). The parameter has a much more significant effect on the resolution in the z direction in (as shown in FIG. 9B) than on the resolution in the x, y direction.

[0062] Thereafter, it is preferable to execute an exemplary procedure to determine the optimized regularization parameters to be used, as shown in step 130 of the method illustrated in FIG. 4A. The details of this exemplary procedure is shown in FIG. 10. Particularly, step 210 shown in FIG. 10 indicates that an L-curve technique can be utilized to set α_a. In one exemplary embodiment of the present invention, the value of α₂ can be substantially the same as that of α₁, thus being substantially similar or equal to a Tiknov regularization technique, at least at this stage. An exemplary graph for the L-curve 250 used by the system and process according to the present invention is illustrated in FIG. 11. Indeed, the L-curve technique is a posterior method which uses only the measurement and the forward model that is illustrated in FIG. 4B. Such forward model can be applied to select the regularization parameter which controls the trade-off between the fidelity to the data and a particular constraint on the result. In FIG. 11, an L-point 260 or the L-curve 250 is provided as an optimized value of α₁. Once α₁ is selected, it is possible to impose α₂ into the interested region.

[0063] In step 220 of the procedure of FIG. 10, the image can then be optically reconstructed using this α_a parameter. Then, in step 230, an appropriate α₂ parameter is determined which can be used for imposing the x-ray constraint. In particular, it is preferably to ascertain such α₂ parameter by compromising between two competing factors: (a) high resolution and contrast, and (b) increasing high frequency noise. This procedure can be performed by plotting a graph 250 of e.g., (contrast 1⁻¹+contrast 2⁻¹)⁻¹ vs. α₂, as illustrated in FIG. 12. The α₂ that maximizes the function may be a preferable choice for reconstructing the final image according to the present invention. Thereafter, in step 240, the final image can be generated using the determined α₂ parameter (e.g., the soft constraint).

[0064] The effects of the artifacts generated by the X-ray constraint can also be reduced with a low-pass filter. It is possible that the optical and X-ray constraints are uncorrelated. FIG. 13 shows a reconstruction imposed by an uncorrelated X-ray constraint. In these illustrations of FIG. 13, the imposed 3-dimensional X-ray image is uncorrelated with the optical heterogeneity. For example, the centers are 3 cm off from one another, while both have a 1 cm radius. The artifacts may be due to high frequency noise, which can be filtered out with an appropriate low-pass filter.

[0065] FIG. 15A shows, a block diagram of a first exemplary embodiment of a system 1500a according to the present invention for generating a resultant image. The system 1500a may include a processing arrangement 1530. The processing arrangement 1530 may be configured to obtain a first image (e.g., an optical diffuse image) and a second image (e.g., an X-ray image, a magnetic resonance image, a functional magnetic resonance image, a computed tomography image, an ultrasound image, etc.) of a subject 1510 (e.g., a human, an animal, etc.) or of a portion 1520 of the subject 1510. For example, the processing arrangement 1530 can simultaneously or sequentially obtain the first and the second images. The processing arrangement 1530 can include a first imaging arrangement 1540 (e.g., a video card), a second processing arrangement 1550 (e.g., a video card), and a processor 1560. For example, the first imaging arrangement 1540 can obtain the first image, and the second imaging arrangement 1550 can obtain the second image.

[0066] The first image may include a first portion of the portion 1520 of the subject 1510 as well as a second portion of the portion 1520 of the subject 1510. Moreover, the processing arrangement 1530 (e.g., the processor 1560 of the processing arrangement 1530) can use the second image (e.g., data associated therewith the) to determine a first probability that indicates that the first portion has a contrast which is greater than or equal to a predetermined contrast (e.g., a contrast associated with an abnormality within the subject 1510, such as a tumor, a lesion, etc.). The processing arrangement 1530 can also use the second image to determine a second probability that indicates that the second portion has a contrast which is greater than or equal to the predetermined contrast, and the second probability may be greater than the first probability, i.e., a higher probability that the second portion of the first image includes the abnormality. For example, the first probability may be about 0%, and the second probability may be about 100%. As such, the second portion may be the area of interest within the subject 1510. Moreover, the processing arrangement 1530 can use the first and second portions of the first image to reconstruct the first image, thereby generating the resultant image.

[0067] For example, the processing arrangement 1530 can reconstruct the first portion based on the first probability to generate a reconstructed first portion of the resultant image, and the processing arrangement 1530 can also reconstruct the second portion based on the second probability to generate a reconstructed second portion of the resultant image. When the first probability is about 0%, the resolution of the reconstructed first portion of the resultant image may be substantially the same as the resolution of the first portion of the first image. This is because the first portion of the first image does not include any area of interest (e.g., does not include the abnormality). When the second probability is about 100%, the resolution of the reconstructed second portion of the resultant image may be greater than the resolution of the second portion of the second image.

[0068] In a variant of this exemplary embodiment of the present invention, the first image can also include a third portion of the subject 1520. For example, the third portion can separate the first portion from the second portion. The third portion can be an outer edge of the abnormality within the subject 1510, and may be subdivided into a plurality of third portions. In this variant, the processing arrangement 1510 can use the second image to determine a third probability indicating that the third portion has a contrast which is greater than or equal to the predetermined contrast. In particular, the third probability may be less than the second probability and greater than the first probability. When the third portion is subdivided into a plurality of third portions, its is possible that each of the third portions may have a different third probability. Nevertheless, each of the third probabilities may be less than the second probability and greater than the first probability.

[0069] For example, when a distance between a particular point within the first image and a center of the abnormality is less than or equal to a first predetermined distance, the probability that the particular point includes the abnormality may be 100%. In are exemplary embodiment of the present invention, the first portion of the first image may include all or substantially all of these particular points, and the first probability may be 100%. When the distance between an intermediate point within the first image and the center of the abnormality is greater than the first predetermined distance but is less than or equal to a second predetermined distance, the probability that the particular point includes the abnormality may be greater than 0% but less than 100%. In another exemplary embodiment of the present invention, the third portion of the first image may include all or substantially all of these intermediate points within the first image, and the third probability may be greater than 0% but less than 100%. For example, the third portion may include the outer edge of the abnormality, and the third probability associated with each of the intermediate points within the third portion may vary depending on the location of the intermediate point within the third portion.

[0070] In particular, the intermediate points which are closest to the center of the abnormality may have an associated third probability equal to 100%−X %, where X is a percentage greater than 0% but less than 50%, and the intermediate points which are closet to the outer edge of the abnormality may have an associated third probability equal to 0%+X %. Moreover, the intermediate points which are positioned between the intermediate points closest to the center of the abnormality and the intermediate points closest to the outer edge may have an associated third probability which is greater than 0%+X % but less than 100%−X %, depending on their exact location within the third portion. When a distance between a further point within the first image and the center of the abnormality is greater than the first and second predetermined distances, the probability that the further point includes the abnormality may be 0%. In a further exemplary embodiment, the second portion of the first image may include all or substantially all of these further points, and the second probability may be 0%.

[0071] In still another exemplary embodiment of the present invention, the reconstruction of the first portion of the first image based on the first probability may include a selection of one or more first regulation parameters α₁ associated with the first probability. For example, the first regulation parameter(s) α₁ may be associated with an optical absorption of the first portion of the first image, and/or an optical scattering of the first portion of the first image. Similarly, the reconstruction of the second portion of the first image based on the second probability may include a selection of one or more second regulation parameters α₂ associated with the second probability. For example, the second regulation parameter(s) α₂ may be associated with an optical absorption of the second portion of the first image, and/or an optical scattering of the second portion of the first image.

[0072] In particular, the first regulation parameter(s) α₁ can control the reconstruction of the first portion, the second regulation parameter(s) α₂ can control the reconstruction of the second portion, and the second regulation parameter may be less than or equal to the first regulation parameter. For example, a normalized value of the first regulation parameter(s) α₁ may be between about 0.1 and about 1, and a normalized value of the second regulation parameter(s) α₂ can be greater than zero and less than or equal to about 0.1. As described above in the Theory Section, the normalized value for the first regulation parameter(s) α₁ may be selected using a L-curve procedure. Moreover, after the normalized value for the first regulation parameter(s) α₁ is selected, the normalized value for the second regulation parameter(s) α₂ can be selected by balancing two inversely related factors. In particular, the such first factor may be the resolution of the reconstructed second portion of the resultant image, and the second such factor may be an amount of noise generated in the reconstructed second portion of the resultant image. For example, increasing the second regulation parameter(s) α₂ decreases the amount of noise generated in the reconstructed second portion, and also decreases the resolution of the reconstructed second portion. Similarly, decreasing the second regulation parameter(s) α₂ increases the resolution of the reconstructed second portion, and also increases the amount of noise generated in the reconstructed second portion. By balancing these two factors, an optimum normalized value for second regulation parameter(s) α₂ may be selected and the objective function can then be minimized.

[0073] FIG. 15B shows, a block diagram of a second exemplary embodiment of a system 1500b according to the present invention for generating a resultant image which includes a processing arrangement 1540. The features and advantages of the system 1500b are substantially the same as the features and advantages of the system 1500a. Therefore, the similar features and advantages of system 1500a and system 1500b are not discussed further with respect to system 1500b. For example, the processing arrangement 1530 may obtain an optical diffuse image, a magnetic resonance image, and a functional magnetic resonance image of the subject 1510 or the portion 1520 of the subject 1510. Moreover, the processing arrangement 1540 can use the second image and the third image to determine the first probability indicating that the first portion of the optical diffuse image has a contrast which is greater than or equal to the predetermined contrast. The processing arrangement 1540 can also use the second image and the third image to determine the second probability indicating that the second portion of the optical diffuse image has a contrast which is greater than or equal to the predetermined contrast, and the second probability is greater than the first probability. Moreover, the processing arrangement uses the first and second portions of the first image to reconstruct the first image, thereby generating the resultant image. In particular, the processing arrangement 1540 reconstructs the first portion based on the first probability to generate the reconstructed first portion of the resultant image. The processing arrangement 1540 can also reconstruct the second portion based on the second probability to generate the reconstructed second portion of the resultant image.

[0074] After the resultant image is generated, the resultant image may be used to determine each of a rate of a flow of blood within the abnormality, a volume of the blood within the abnormality, and a deoxyhemoglobin concentration within the abnormality. Based on the data associated with the flow of the blood, the volume of the blood, and the deoxyhemoglobin concentration within the abnormality, the amount of oxygen consumed by the abnormality then may be determined using any known technique for determining oxygen consumption.

[0075] FIG. 16A shows, a flowchart of a second exemplary embodiment of a method according to the present invention for generating the resultant image. In step 1610, the first and second images are obtained with the first image including the first portion of the subject and the second portion of the subject. The first and second images can be different image types. In steps 1620 and 1630, the first and second probabilities described ______ can be determined, respectively. Moreover, in step 1640, the first and second portions of the first image are reconstructed based on the first and second probabilities, respectively, to generate the resultant image. For example, referring to FIG. 16B which shows the exemplary details of step 1640, step 1640a provide that the first regularization parameter α₁ is selected, and step 1640b provides that, the second regularization parameter α₂ is selected. FIG. 16C shows exemplary details of step 1640, step 1640a′ provides that the first regularization parameter α₁ is selected using the L-Curve procedure, and step 1640b provides that, the second regularization parameter α₂ is selected by balancing the resolution of the second portion of the resultant image and the noise generated in the second portion of the resultant image.

[0076] FIG. 17 shows a flowchart of a third exemplary embodiment of the method according to the present invention for generating the resultant image is depicted. In step 1710, the first and second images are obtained, and in steps 1720, 1730, and 1740 the first, second, and third probabilities are determined, respectively. For example, the third probability may include a plurality of third probabilities, and each of the third probabilities may correspond to one of the third portions of the first image. Moreover, in step 1750, the first, second, and at least one third portions of the first image are reconstructed based on the first, second, and third probabilities, respectively, to generate the resultant image.

[0077] FIG. 18 illustrates a flowchart of a fourth exemplary embodiment of the method according to the present invention for generating the resultant image is depicted. In step 1810, the diffuse optical image, the magnetic resonance image, and the functional magnetic resonance image are obtained. Specifically, the diffuse optical image includes the first portion and the second portion. In steps 1820 and 1830, the first and second probabilities are determined, respectively. Moreover, in step 1840, the first and second portions of the diffuse optical image are reconstructed based on the first and second probabilities, respectively, to generate the resultant diffuse optical image. Then, in step 1850, the rate of flow of blood, the volume of the blood, and the deoxyhemoglobin concentration within the abnormality is determined using the resultant diffuse optical image. Finally, in step 1860, the amount of oxygen consumed by the abnormality is determined based on the data associated with the rate of flow of blood, the volume of the blood, and the deoxyhemoglobin concentration within the abnormality using a known technique.

[0078] While the invention has been described in connection with preferred embodiments, it will be understood by those skilled in the art that other variations and modifications of the preferred embodiments described above may be made without departing from the scope of the invention. Other embodiments will be apparent to those skilled in the art from a consideration of the specification or practice of the invention disclosed herein. It is intended that the specification and the described examples are consider exemplary only, with the true scope of the invention indicated by the following claims.