Distributed Graph Regularized Denoising via Constrained Chebyshev Polynomials

The problem of denoising signals, defined over graph domains, using a regularization framework, is considered here. Using the
$L^{2}$
norm, the optimum denoising operator involves a matrix inverse. Approximation of the operator via matrix polynomial is commonly used to achieve an efficient distributed implementation. We first propose a modification to the fidelity term in the regularization framework. Based on the assumption of signal smoothness, weighting is applied to the frequency components of the noisy signal. We then propose an extension to the classical approximation using Chebyshev polynomials, by imposing linear constraints on the coefficients of the Chebyshev series. We will show that the constrained coefficients are related to the unconstrained coefficients via an affine transformation. Performance evaluation of the proposed distributed filters for denoising, using real-world datasets, is presented. Comparison with the classical filters is provided.