Constructing an Interpretable Deep Denoiser by Unrolling Graph Laplacian Regularizer
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 $\boldsymbol \Psi^{-1}$. 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.
Code (0)
등록된 구현이 없습니다.
Tasks
DenoisingImage DenoisingSimilar Papers 제목 키워드 기반
Lightweight Transformer for EEG Classification via Balanced Signed Graph Algorithm Unrolling
Samples of brain signals collected by EEG sensors have inherent anti-correlations that are well modeled by negative edges in a finite graph. To differentiate epilepsy patients from healthy subjects using collected EEG si…
Binary ClassificationGraph Signal Restoration Using Nested Deep Algorithm Unrolling
Graph signal processing is a ubiquitous task in many applications such as sensor, social, transportation and brain networks, point cloud processing, and graph neural networks. Often, graph signals are corrupted in the se…
DenoisingRolling Shutter CorrectionGraph Unrolling Networks: Interpretable Neural Networks for Graph Signal Denoising
We propose an interpretable graph neural network framework to denoise single or multiple noisy graph signals. The proposed graph unrolling networks expand algorithm unrolling to the graph domain and provide an interpreta…
DenoisingGraph Neural NetworkRolling Shutter CorrectionInterpretable Lightweight Transformer via Unrolling of Learned Graph Smoothness Priors
We build interpretable and lightweight transformer-like neural networks by unrolling iterative optimization algorithms that minimize graph smoothness priors -- the quadratic graph Laplacian regularizer (GLR) and the $\el…
Graph LearningUnrolling Plug-and-Play Gradient Graph Laplacian Regularizer for Image Restoration
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 o…
DenoisingGraph LearningImage Restoration