  Inspired by group-based sparse coding, recently proposed group sparsity
residual (GSR) scheme has demonstrated superior performance in image
processing. However, one challenge in GSR is to estimate the residual by using
a proper reference of the group-based sparse coding (GSC), which is desired to
be as close to the truth as possible. Previous researches utilized the
estimations from other algorithms (i.e., GMM or BM3D), which are either not
accurate or too slow. In this paper, we propose to use the Non-Local Samples
(NLS) as reference in the GSR regime for image denoising, thus termed GSR-NLS.
More specifically, we first obtain a good estimation of the group sparse
coefficients by the image nonlocal self-similarity, and then solve the GSR
model by an effective iterative shrinkage algorithm. Experimental results
demonstrate that the proposed GSR-NLS not only outperforms many
state-of-the-art methods, but also delivers the competitive advantage of speed.
