The springback penalty for robust signal recovery

We propose a new penalty, the springback for constructing models to recover an unknown signal from incomplete and inaccurate measurements. Mathematically, penalty is weakly convex function. It bears various theoretical computational advantages of both benchmark $\ell_1$ many its non-convex surrogates that have been well studied in literature. establish exact stable recovery theory model using sparse nearly signals, respectively, derive easily implementable difference-of-convex algorithm. In particular, we show superiority some existing with sharper bound scenarios where level measurement noise large or amount measurements limited. also demonstrate numerical robustness regardless varying coherence sensing matrix. The particularly favorable scenario are collected by coherence-hidden -static hardware due guarantee severe measurements, tractability, ill-conditioned matrices.