We present a new algorithm and the corresponding convergence analysis for theregularization of linear inverse problems with sparsity constraints, applied toa new generalized sparsity promoting functional. The algorithm is based on theidea of iteratively reweighted least squares, reducing the minimization atevery iteration step to that of a functional including only $\ell_2$-norms.This amounts to smoothing of the absolute value function that appears in thegeneralized sparsity promoting penalty we consider, with the smoothing becomingiteratively less pronounced. We demonstrate that the sequence of iterates ofour algorithm converges to a limit that minimizes the original functional.
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