Doubly iteratively reweighted algorithm for constrained compressed sensing models

We propose a new algorithmic framework for constrained compressed sensing models that admit nonconvex sparsity-inducing regularizers including the log-penalty function as objectives, and loss functions such Cauchy Tukey biweight in constraint. Our employs iteratively reweighted $$\ell _1$$ _2$$ schemes to construct subproblems can be efficiently solved by well-developed solvers basis pursuit denoising SPGL1 van den Berg Friedlander (SIAM J Sci Comput 31:890-912, 2008). termination criterion subproblem allows them return an infeasible solution, with suitably constructed feasible point satisfying descent condition. The construction step is key establishing well-definedness of our proposed algorithm, we also prove any accumulation this sequence points stationary model, under suitable assumptions. Finally, compare numerically algorithm (with or alternating direction method multipliers) against SCP $$_\textrm{ls}$$ Yu et al. Optim 31: 2024-2054, 2021) on solving objective constraint, badly scaled measurement matrices. computational results show approaches solutions better recovery errors, are always faster.