Sharpening Sparse Regularizers via Smoothing

Non-convex sparsity-inducing penalties outperform their convex counterparts, but generally sacrifice the cost function convexity. As a middle ground, we propose sharpening sparse regularizers (SSR) framework to design non-separable non-convex that induce sparsity more effectively than such as l 1 and nuclear norms, without sacrificing The overall problem convexity is preserved by exploiting data fidelity relative strong constructs difference of functions, namely between smoothed versions. We generalized infimal convolution smoothing technique obtain Furthermore, SSR recovers generalizes several in literature special cases. applicable any regularized least squares ill-posed linear inverse problem. Beyond squares, can be extended accommodate Bregman divergence, other structures low-rankness. optimization formulated saddle point problem, solved scalable forward-backward splitting algorithm. effectiveness demonstrated numerical experiments different applications.