Solving robust regularization problems using iteratively re-weighted least squares

Many computer vision problems are formulated as an objective function consisting of a sum of functions. In the case of ill-constrained problems, regularization terms are included in the objective function to reduce the ambiguity and noise in the solution. The most commonly used regularization terms are the L2 norm and the L1 norm. Since the last two decades, the class of regularized problems, especially the L1-regularized problems, has received much attention but still many regularized problems are either difficult to solve, or require complex optimization techniques. We propose a method based on an Iteratively Re-weighted Least Squares approach to minimize an objective function comprising a mixture of m-estimator regularization terms. In addition to the proof of convergence of the algorithm to the desired minimum, we show the applicability of the proposed algorithm by solving the problems of edge-preserved image denoising and image super-resolution. In both the cases, our experimental results show that the proposed algorithm gives superior results to the state-of-Art regularization methods.