Speckle noise removal using a two-step weighted robust regression

The speckle usually degrades the signal quality for coherent detection or imaging. In this paper, under the single-image constraint, we propose a two-step weighted robust regression method for speckle removal, where the first step is to smooth the speckle-noisy image by means of block matching and 3D filtering (BM3D), and the second step is further to apply a weighted robust regression to discriminate between the signal and residual speckle and to recover the edge information. Theoretical demonstration is presented, and experimental results with laser illumination are shown and compared to other competing methods. The experiments show that our method has robustness and prominent improvement of 12 similar to 19% in the speckle removal task.