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1. SYMMETRIC SMOOTHING FILTERS FROM GLOBAL CONSISTENCY
CONSTRAINTS
ABSTRACT
Many patch-based image denoising methods can be viewed as data-dependent smoothing
filters that carry out a weighted averaging of similar pixels. It has recently been argued that these
averaging filters can be improved using their doubly stochastic approximation, which are
symmetric and stable smoothing operators. In this paper, we introduce a simple principle of
consistency that argues that the relative similarities between pixels as imputed by the averaging
matrix should be preserved in the filtered output. The resultant consistency filter has the
theoretically desirable properties of being symmetric and stable, and is a generalized doubly
stochastic matrix. In addition, we can also interpret our consistency filter as a specific form of
Laplacian regularization. Thus, our approach unifies two strands of image denoising methods,
i.e., symmetric smoothing filters and spectral graph theory. Our consistency filter provides high-
quality image denoising and significantly outperforms the doubly stochastic version. We present
a thorough analysis of the properties of our proposed consistency filter and compare its
performance with that of other significant methods for image denoising in the literature.