We extend a recently proposed alternating minimization algorithm to the case of recovering blurry multichannel (color) images corrupted by impulsive rather than Gaussian noise. The algorithm minimizes the sum of a multichannel extension of total variation (TV), either isotropic or anisotropic, and a data fidelity term measured in the L1-norm. We derive the algorithm by applying the well-known quadratic penalty function technique and prove attractive convergence properties including finite convergence for some variables and global q-linear convergence. Under periodic boundary conditions, the main computational requirements of the algorithm are fast Fourier transforms and a low-complexity Gaussian elimination procedure. Numerical results on images with different blurs and impulsive noise are presented to demonstrate the efficiency of the algorithm. In addition, it is numerically compared to a recently proposed algorithm that uses a linear program and an interior point method for recovering grayscale images.
TR 08-12, Department of Computational and Applied Mathematics, Rice University