Data-driven System Matrix Manipulation Enabling Fast Functional Imaging in Tomography

Tomographic imaging modalities are described by large system matrices. To improve the temporal resolution of functional imaging in tomography, sparse spatial sampling is often employed, which degrades the system matrix and introduces artifacts in reconstructed images. Various existing techniques improve the image quality without correcting the system matrix and have limitations. Here, we compress the system matrix to improve computational efficiency (e.g., 42 times) using singular value decomposition and fast Fourier transform. Enabled by the efficiency, we propose fast sparsely sampling functional imaging by incorporating a densely sampled prior image into the system matrix, which maintains the critical linearity while mitigating artifacts. We demonstrate the methods in 3D photoacoustic computed tomography with significantly improved image quality and clarify their applicability to X-ray CT and radial-sampling MRI due to the similarities in system matrices.