Unrolling Plug-and-Play Gradient Graph Laplacian Regularizer for Image Restoration (2407.01469v3)

Abstract: Generic deep learning (DL) networks for image restoration like denoising and interpolation lack mathematical interpretability, require voluminous training data to tune a large parameter set, and are fragile in the face of covariate shift. To address these shortcomings, we build interpretable networks by unrolling variants of a graph-based optimization algorithm of different complexities. Specifically, for a general linear image formation model, we first formulate a convex quadratic programming (QP) problem with a new $\ell_2$-norm graph smoothness prior called gradient graph Laplacian regularizer (GGLR) that promotes piecewise planar (PWP) signal reconstruction. To solve the posed unconstrained QP problem, instead of computing a linear system solution straightforwardly, we introduce a variable number of auxiliary variables and correspondingly design a family of ADMM algorithms. We then unroll them into variable-complexity feed-forward networks, amenable to parameter tuning via back-propagation. More complex unrolled networks require more labeled data to train more parameters, but have better overall performance. The unrolled networks have periodic insertions of a graph learning module, akin to a self-attention mechanism in a transformer architecture, to learn pairwise similarity structure inherent in data. Experimental results show that our unrolled networks perform competitively to generic DL networks in image restoration quality while using only a fraction of parameters, and demonstrate improved robustness to covariate shift.