An Iteratively Reweighted Least Squares Algorithm for Sparse Regularization
It provides a new algorithm with theoretical convergence for a generalized sparsity-promoting functional, but the contribution is incremental as it extends existing IRLS methods.
The paper presents an iteratively reweighted least squares algorithm for sparse regularization of linear inverse problems, with convergence guarantees to a minimizer of the original functional.
We present a new algorithm and the corresponding convergence analysis for the regularization of linear inverse problems with sparsity constraints, applied to a new generalized sparsity promoting functional. The algorithm is based on the idea of iteratively reweighted least squares, reducing the minimization at every iteration step to that of a functional including only $\ell_2$-norms. This amounts to smoothing of the absolute value function that appears in the generalized sparsity promoting penalty we consider, with the smoothing becoming iteratively less pronounced. We demonstrate that the sequence of iterates of our algorithm converges to a limit that minimizes the original functional.