Demystifying Symmetric Smoothing Filters

—Many patch-based image denoising algorithms can be formulated as applying a smoothing filter to the noisy image. Expressed as matrices, the smoothing filters must be row normalized so that each row sums to unity. Surprisingly, if we apply a column normalization before the row normalization, the performance of the smoothing filter can often be significantly improved. Prior works showed that such performance gain is related to the Sinkhorn-Knopp balancing algorithm, an iterative procedure that symmetrizes a row-stochastic matrix to a doublystochastic matrix. However, a complete understanding of the performance gain phenomenon is still lacking. In this paper, we study the performance gain phenomenon from a statistical learning perspective. We show that SinkhornKnopp is equivalent to an Expectation-Maximization (EM) algorithm of learning a Product of Gaussians (PoG) prior of the image patches. By establishing the correspondence between the steps of Sinkhorn-Knopp and the EM algorith...

• Type: Journal
• Year: 2016
• Where: CORR
• Authors: Stanley H. Chan, Todd E. Zickler, Yue M. Lu
• Keywords: CORR 2016, Education