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CORR
2016
Springer

Demystifying Symmetric Smoothing Filters

8 years 7 months ago
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...
Stanley H. Chan, Todd E. Zickler, Yue M. Lu
Added 01 Apr 2016
Updated 01 Apr 2016
Type Journal
Year 2016
Where CORR
Authors Stanley H. Chan, Todd E. Zickler, Yue M. Lu
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