Sparse representation of measurements
A computer system that performs a sparsity technique is described. During operation, the computer system accesses or obtains information associated with non-invasive measurements performed on at least an individual, historical non-invasive measurements, and a dictionary of predetermined features or basis functions associated with the historical non-invasive measurements. Note that the non-invasive measurements and the historical non-invasive measurements may include or correspond to magnetic resonance (MR) measurements. For example, the MR measurements may include magnetic resonance imaging (MRI) scans. Then, the computer system updates the dictionary of predetermined features based at least in part on the non-invasive measurements and the historical non-invasive measurements, where the updating includes performing a minimization technique with a cost function having an L2-norm term and an L0-norm term. Next, the computer system determines weights associated with features in the updated dictionary of predetermined features based at least in part on the non-invasive measurements.
1. A method of performing a sparsity technique, comprising:
by a computer system:
updating a dictionary of predetermined features based at least in part on non-invasive measurements performed on an individual and historical non-invasive measurements;
determining weights associated with features in an updated dictionary of predetermined features based at least in part on the non-invasive measurements;
computing or selecting a sampling pattern based at least in part on the non-invasive measurements and the historical non-invasive measurements;
obtaining an image of at least a portion of the individual by performing additional non-invasive measurements based at least in part on the computed or selected sampling pattern, wherein the image comprises a sub-sampled or a compressed image; and
reconstructing a second image based at least in part on the image, the updated dictionary of predetermined features and the determined weights.
2. The method of claim 1 , wherein the non-invasive measurements and the historical non-invasive measurements comprise or correspond to magnetic-resonance (MR) measurements.
3. The method of claim 1 , wherein the updating comprises performing a minimization technique with a cost function having an L2-norm term and an L0-norm term.
4. The method of claim 1 , wherein the non-invasive measurements and the historical non-invasive measurements comprises magnetic-resonance (MR) parameters associated with voxels in the individual.
5. The method of claim 4 , wherein the MR parameters comprise: a density of a type of nuclei, a longitudinal relaxation time along a direction parallel to an external magnetic field and a transverse relaxation time along a direction perpendicular to the external magnetic field.
6. The method of claim 4 , wherein the non-invasive measurement comprise at least a component of a magnetization associated with the individual, and the method comprises:
calculating at least a predicted component of the magnetization for the voxels associated with the individual based at least in part on the measured component of the magnetization, a forward model, an external magnetic field and a radio frequency (RF) pulse sequence; and
solving an inverse problem by iteratively modifying the MR parameters associated with the voxels in the forward model until a difference between the predicted component of the magnetization and the measured component of the magnetization is less than a predefined value.
7. The method of claim 1 , wherein the historical non-invasive measurements are associated with the individual or a group of individuals.
8. The method of claim 7 , wherein the group of individuals excludes the individual.
9. The method of claim 1 , wherein determining the weights comprises a gradient-descent technique.
10. The method of claim 1 , wherein the updated dictionary of predetermined features correspond to a portion of an anatomy of the individual.
11. A computer system, comprising:
an interface circuit;
a processor coupled to the interface circuit; and
memory, coupled to the processor, storing program instructions, wherein, when executed by the processor, the program instructions cause the computer system to perform operations comprising:
updating a dictionary of predetermined features based at least in part on non-invasive measurements performed on an individual and historical non-invasive measurements;
determining weights associated with features in the updated dictionary of predetermined features based at least in part on the non-invasive measurements;
computing or selecting a sampling pattern based at least in part on the non-invasive measurements and the historical non-invasive measurements;
obtaining an image of at least a portion of the individual by performing additional non-invasive measurements based at least in part on the computed or selected sampling pattern, wherein the image comprises a sub-sampled or a compressed image; and
reconstructing a second image based at least in part on the image, the updated dictionary of predetermined features and the determined weights.
12. The computer system of claim 11 , wherein the non-invasive measurements and the historical non-invasive measurements comprise or correspond to magnetic-resonance (MR) measurements.
13. The computer system of claim 11 , wherein the non-invasive measurements and the historical non-invasive measurements comprises magnetic-resonance (MR) parameters associated with voxels in the individual.
14. The computer system of claim 11 , wherein the updating comprises performing a minimization technique with a cost function having an L2-norm term and an L0-norm term.
15. The computer system of claim 13 , wherein the non-invasive measurement comprise at least a component of a magnetization associated with the individual, and the operations comprise:
calculating at least a predicted component of the magnetization for the voxels associated with the individual based at least in part on the measured component of the magnetization, a forward model, an external magnetic field and a radio frequency (RF) pulse sequence; and
solving an inverse problem by iteratively modifying the MR parameters associated with the voxels in the forward model until a difference between the predicted component of the magnetization and the measured component of the magnetization is less than a predefined value.
16. The computer system of claim 11 , wherein the historical non-invasive measurements are associated with the individual or a group of individuals; and
wherein the group of individuals excludes the individual.
17. The computer system of claim 11 , wherein determining the weights comprises a gradient-descent technique.
18. The computer system of claim 11 , wherein the updated dictionary of predetermined features correspond to a portion of an anatomy of the individual.
19. A non-transitory computer-readable storage medium for use in conjunction with a computer system, the computer-readable storage medium configured to store a program module that, when executed by the computer system, causes the computer system to perform operations comprising:
updating a dictionary of predetermined features based at least in part on non-invasive measurements performed on an individual and historical non-invasive measurements;
determining weights associated with features in the updated dictionary of predetermined features based at least in part on the non-invasive measurements;
computing or selecting a sampling pattern based at least in part on the non-invasive measurements and the historical non-invasive measurements;
obtaining an image of at least a portion of the individual by performing additional non-invasive measurements based at least in part on the computed or selected sampling pattern, wherein the image comprises a sub-sampled or a compressed image; and
reconstructing a second image based at least in part on the image, the updated dictionary of predetermined features and the determined weights.
20. The computer-readable storage medium of claim 19 , wherein the non-invasive measurements and the historical non-invasive measurements comprises magnetic-resonance (MR) parameters associated with voxels in the individual.