Adaptive Robust Low-Rank 2-D Reconstruction with Steerable Sparsity

Existing image reconstruction methods frequently improve their robustness by using various nonsquared loss functions, which are still potentially sensitive to the outliers. More specifically, when certain samples in data sets encounter severe contamination, these methods cannot identify and filter out the ill ones, and thus lead to the functional degeneration of the associated models. To address this issue, we propose a general framework, named robust and sparse weight learning (RSWL), to compute the adaptive weights based on an objective for robustness and sparsity. More importantly, the degree of the sparsity is steerable, such that only k well-reserved samples are activated during the optimization of our model. As a result, the severely polluted or damaged samples are eliminated, and the robustness is ensured. The framework is further leveraged against a 2-D image reconstruction task. Theoretical analysis and extensive experiments are presented to demonstrate the superiority of the proposed method.