  Sparsity promoting functions (SPFs) are commonly used in optimization
problems to find solutions which are assumed or desired to be sparse in some
basis. For example, the l1-regularized variation model and the
Rudin-Osher-Fatemi total variation (ROF-TV) model are some of the most
well-known variational models for signal and image denoising, respectively.
However, recent work demonstrates that convexity is not always desirable in
sparsity promoting functions. In this paper, we replace convex SPFs with their
induced nonconvex SPFs and develop algorithms for the resulting model by
exploring the intrinsic structures of the nonconvex SPFs. We also present
simulations illustrating the performance of the SPF and the developed
algorithms in image denoising.
