Data-driven system matrix manipulation enabling fast functional imaging and intra-image nonrigid motion correction in tomography

Tomographic imaging modalities are described by large system matrices. Sparse sampling and tissue motion degrade system matrix and image quality. Various existing techniques improve the image quality without correcting the system matrices. Here, we compress the system matrices to improve computational efficiency (e.g., 42 times) using singular value decomposition and fast Fourier transform. Enabled by the efficiency, we propose (1) fast sparsely sampling functional imaging by incorporating a densely sampled prior image into the system matrix, which maintains the critical linearity while mitigating artifacts and (2) intra-image nonrigid motion correction by incorporating the motion as subdomain translations into the system matrix and reconstructing the translations together with the image iteratively. We demonstrate the methods in 3D photoacoustic computed tomography with significantly improved image qualities and clarify their applicability to X-ray CT and MRI or other types of imperfections due to the similarities in system matrices.