An algorithm for total variation regularization in high-dimensional linear problems

Abstract

This paper describes an iterative algorithm for high-dimensional linear inverse problems, which is regularized by a differentiable discrete approximation of the total variation (TV) penalty. The algorithm is an interlaced iterative method based on optimization transfer with a separable quadratic surrogate for the TV penalty. The surrogate cost function is optimized using the block iterative regularized algebraic reconstruction technique (RSART). A proof of convergence is given and convergence is illustrated by numerical experiments with simulated parallel-beam computerized tomography (CT) data. The proposed method provides a block-iterative and convergent, hence efficient and reliable, algorithm to investigate the effects of TV regularization in applications such as CT.