A TV-minimization image-reconstruction algorithm without system matrix

Total Variation (TV) minimization algorithm is a classical compressed sensing (CS) based iterative image reconstruction algorithm that can accurately reconstruct images from sparse-view projections in computed tomography (CT). However, the system matrix used in the algorithm is often too large to be stored in computer memory. The purpose of this study is to investigate a new TV algorithm based on image rotation and without system matrix to avoid the memory requirement of system matrix.

Without loss of generality, a rotation-based adaptive steepest descent-projection onto convex sets (R-ASD-POCS) algorithm is proposed and tested to solve the TV model in parallel beam CT. Specifically, simulation experiments are performed via the Shepp-Logan, FORBILD and real CT image phantoms are used to verify the inverse-crime capability of the algorithm and evaluate the sparse reconstruction capability and the noise suppression performance of the algorithm.

Experimental results show that the algorithm can achieve inverse-crime, accurate sparse reconstruction and thus accurately reconstruct images from noisy projections. Compared with the classical ASD-POCS algorithm, the new algorithm may yield the similar image reconstruction accuracy without use of the huge system matrix, which saves the computational memory space significantly. Additionally, the results also show that R-ASD-POCS algorithm is faster than ASD-POCS.

The proposed new algorithm can effectively solve the problem of using huge memory in large scale and iterative image reconstruction. Integrating with ASD-POCS frame, this no-system-matrix based scheme may be readily extended and applied to any iterative image reconstructions.