An iterative algorithm for nonlinear inverse problems with joint sparsity constraints in vector-valued regimes and an application to color image inpainting

This paper is concerned with nonlinear inverse problems where data and solution are vector valued and, moreover, where the solution is assumed to have a sparse expansion with respect to a preassigned frame. We especially focus on such problems where the different channels of the solution exhibit a common or so-called joint sparsity pattern encoding special characteristics of the function under consideration ( e. g. a coupling of non-vanishing channel components). Quite recently, an iterative strategy for linear inverse problems with such joint sparsity constraints was presented. Here, we develop an iterative approach for nonlinear inverse problems for which we show norm convergence and regularization properties. The focus throughout the paper is in the context of color image inpainting/recolorization.