A Computational Algorithm for Minimizing Total Variation in Image Restoration

Abstract

A reliable and efficient computational algorithm for restoring blurred and noisy images is proposed. The restoration process is based on the minimal total variation principle introduced by Rudin et al [1], [2], [3]. For discrete images, the proposed algorithm minimizes a piecewise linear l 1 function (a measure of total variation) subject to a single 2-norm inequality constraint (a measure of data fit). The algorithm starts by finding a feasible point for the inequality constraint using a (partial) conjugate gradient method. This corresponds to a deblurring process. Noise and other artifacts are removed by a subsequent total variation minimization process. The use of the linear l 1 objective function for the total variation measurement leads to a simplier computational algorithm. Both the steepest descent and an affine scaling Newton method are considered for solving this constrained piecewise linear l 1 minimization problem. The resulting algorithm, when viewed as an image restoratio..