Iterative reconstruction in image formation
The use of the channelized preconditioners in iterative reconstruction is disclosed. In certain embodiments, different channels correspond to different frequency sub-bands and the output of the different channels can be combined to update an image estimate used in the iterative reconstruction process. While individual channels may be relatively simple, the combined channels can represent complex spatial variant operations. The use of channelized preconditioners allows empirical adjustment of individual channels.
1. An image formation method, comprising:
generating an image estimate with a processing component in communication with an imaging system;
simulating an expected projection based on the image estimate;
acquiring a set of measured projection data with the imaging system;
comparing, with the processing component, the expected projection to the set of measured projection data based on a cost function;
determining, with the processing component, a gradient vector based on the cost function that incorporates noise characteristics or other models of the imaging system;
implementing a multi-channel preconditioner on two or more channels such that each channel is processed independent of the other channels;
applying, with the processing component, the multi-channel preconditioner to the gradient vector;
combining, with the processing component, the outputs of the multi-channel preconditioner to generate a transformed gradient vector; and
updating, with the processing component, the image estimate using the transformed gradient vector.
2. The image formation method of claim 1 , wherein the expected projection is simulated based on a set of system optics associated with the imaging system.
3. The image formation method of claim 1 , wherein the gradient vector is determined with respect to a cost function.
4. The image formation method of claim 1 , wherein the multi-channel preconditioner comprises two or more linear or non-linear components.
5. The image formation method of claim 4 , wherein each component represents one or more of high-pass, low-pass, band-pass, or all-pass frequency channels, and wherein the frequency channels can be isotropic, approximately isotropic, or anisotropic.
6. The image formation method of claim 4 , wherein each component represents one of an analytic filtering operation, an iterative filtering operation, or a matrix inversion operation.
7. The image formation method of claim 4 , wherein one or more components are modulated by spatial weights or masks.
8. The image formation method of claim 4 , wherein one or more components comprise a diagonal matrix.
9. The image formation method of claim 4 , wherein one or more components comprise an image-space filter or a Fourier space filter.
10. The image formation method of claim 9 , wherein the image space filter or the Fourier space filter are in two-dimensions or three-dimensions.
11. The image formation method of claim 4 , wherein one or more components comprise a wavelet transform.
12. The image formation method of claim 4 , wherein each component can operate at a different resolution or different sizes of filter footprints.
13. The image formation method of claim 1 , wherein the multi-channel preconditioner can be combined with one or more of a conjugate gradient algorithm, an ordered subset algorithm, a Barzilai-Borwein algorithm, a Nesterov algorithm, or a variable-splitting -based algorithm.
14. The image formation method of claim 1 , wherein the multi-channel preconditioner can be nested with other components and used recursively.
15. The image formation method of claim 1 , wherein single or multiple search directions are utilized each iteration.
16. The image processing method of claim 1 , wherein a step size in each iteration is computed to provide conjugacy of the search directions with respect to a Hessian matrix.
17. The image processing method of claim 1 , comprising iterating the steps of simulating, comparing, determining, implementing, combining, applying, and updating, until a cost function is satisfied.
18. An image formation system for use in iterative reconstruction, comprising:
a processing component in communication with an imaging system and configured to access acquired data from an imaging device; and
a memory configured to store one or more routines which, when executed by the processor, cause acts to be performed comprising:
generating an image estimate with the processing component;
simulating an expected projection based on the image estimate;
acquiring a set of measured projection data with the imaging system;
comparing, with the processing component, expected projection to the set of measured projection data based on a cost function;
determining, with the processing component, a gradient vector based on the cost function that incorporates noise characteristics or other models of the imaging system;
implementing a multi-channel preconditioner on two or more channels such that each channel is processed independent of the other channels;
applying, with the processing component, the multi-channel preconditioner to the gradient vector;
combining, with the processing component, the outputs of the multi-channel preconditioner to generate a transformed gradient vector; and
updating, with the processing component, the image estimate using the transformed gradient vector.
19. The image formation system of claim 18 , wherein the multi-channel preconditioner comprises two or more linear or non-linear components.
20. The image formation system of claim 19 , wherein each component represents one or more of a high-pass, low-pass, band-pass, or all-pass frequency channels, and wherein the frequency channels can be isotropic, approximately isotropic, or anisotropic.
21. The image formation system of claim 19 , wherein each component represents one of an analytic filtering operation, an iterative filtering operation, or a matrix inversion operation.
22. The image formation system of claim 19 , wherein one or more components are modulated by spatial weights or masks.
23. The image formation system of claim 19 , wherein one or more components comprise a diagonal matrix.
24. The image formation system of claim 19 , wherein one or more components comprise an image-space filter or a Fourier space filter.
25. One or more non-transitory computer-readable media encoding routines which, when executed, cause acts to be performed comprising:
generating an image estimate with a processing component in communication with an imaging system;
simulating an expected projection based on the image estimate;
acquiring a set of measured projection data with the imaging system;
comparing, with the processing component, the expected projection to the set of measured projection data based on a cost function;
determining, with the processing component a gradient vector based on the cost function that incorporates noise characteristics or other models of the imaging system;
implementing a multi-channel preconditioner on two or more channels such that each channel is processed independent of the other channels;
applying, with the processing component, the multi-channel preconditioner to the gradient vector;
combining, with the processing component, the outputs of the multi-channel preconditioner to generate a transformed gradient vector; and
updating, with the processing component, the image estimate using the transformed gradient vector.
26. The one or more non-transitory computer-readable media of claim 25 , wherein the multi-channel preconditioner comprises two or more linear or non-linear components.
27. The one or more non-transitory computer-readable media of claim 26 , wherein each component represent one or more of a high-pass, low-pass, band-pass, or all-pass frequency channels, and wherein the frequency channels can be isotropic, approximately isotropic, or anisotropic.
28. The one or more non-transitory computer-readable media of claim 26 , wherein each component represents one of an analytic filtering operation, an iterative filtering operation, or a matrix inversion operation.
29. The one or more non-transitory computer-readable media of claim 26 , wherein one or more components are modulated by spatial weights or masks.
30. The one or more non-transitory computer-readable media of claim 26 , wherein one or more components comprise an image-space filter or a Fourier space filter.