Performance analysis of denoising with low-rank and sparsity constraints

Recent denoising methods that exploit the low-rank property and sparsity of the underlying signals have produced impressive empirical results in various imaging applications. However, the fundamental limits of their denoising capability have not been systematically analyzed. This paper presents an analysis of the denoising effects of imposing low-rank and sparsity constraints. Specifically, we use the constrained Cramér-Rao lower bound to derive upper bounds on the maximum noise reduction when applying these two constraints, individually or simultaneously. We also perform numerical simulations to compare the theoretical bounds with noise reductions from practical denoising methods. These results should provide useful insights into the utility of low-rank and sparsity constraints for denoising.