A Preconditioning Approach To Optimizing Sensing Matrix For Improved Compressed Sensing CT Reconstruction

Compressed sensing (CS) exploiting inherent sparsity prior of signals has been proven effective for sparse-view computed tomography (CT) image reconstruction from undersampled projection data. However, most CS-based CT studies focused on formulating different sparsity regularizers, e.g., total variation (TV) minimization, and neglect design of an incoherent sensing matrix - a key factor of CS performance. The sensing matrix formed by an incomplete set of Radon projections in CT typically exhibits large coherence. In this paper, we propose a novel method for optimizing the sensing matrix via preconditioning to improve CS-CT reconstruction. A well-conditioned preconditioner is designed to optimally reduce the coherence of the sensing matrix and thus improving the CS systems. The desired preconditioner is obtained by solving a nonconvex optimization problem via gradient descent method. The preconditioned systems solved by TV-based sparse recovery algorithms can provide better reconstruction accuracy with fewer measurements even in noisy settings. Evaluated on brain and COVID-19 chest CT datasets, the proposed method when used for preconditioning of Radon sensing matrix reconstructed images with substantially higher quality with faster speed than baselines without preconditioning.