Constructing an Interpretable Deep Denoiser by Unrolling Graph Laplacian Regularizer

Abstract

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An image denoiser can be used for a wide range of restoration problems via the Plug-and-Play (PnP) architecture. In this paper, we propose a general framework to build an interpretable graph-based deep denoiser (GDD) by unrolling a solution to a maximum a posteriori (MAP) problem equipped with a graph Laplacian regularizer (GLR) as signal prior. Leveraging a recent theorem showing that any (pseudo-)linear denoiser $\boldsymbol{\Psi}$, under mild conditions, can be mapped to a solution of a MAP denoising problem regularized using GLR, we first initialize a graph Laplacian matrix $\mathbf{L}$ via truncated Taylor Series Expansion (TSE) of $\Psi^{-1}$. Then, we compute the MAP linear system solution by unrolling iterations of the conjugate gradient (CG) algorithm into a sequence of neural layers as a feed-forward network—one that is amenable to parameter tuning. The resulting GDD network is “graph-interpretable”, low in parameter count, and easy to initialize thanks to $\mathbf{L}$ derived from a known well-performing denoiser $\boldsymbol{\Psi}$. Experimental results show that GDD achieves competitive image denoising performance compared to competitors, but employing far fewer parameters, and is more robust to covariate shift.