Graph Neural Net Using Analytical Graph Filters and Topology Optimization for Image Denoising

Abstract

While convolutional neural nets (CNN) have achieved remarkable performance for a wide range of inverse imaging applications, the filter coefficients are computed in a purely data-driven manner and are not explainable. Inspired by an analytically derived CNN by Hadji et al., in this paper we construct a new layered graph convolutional neural net (GCNN) using GraphBio as our graph filter. Unlike convolutional filters in previous GNNs, our employed GraphBio is analytically defined and requires no training, and we optimize the end-to-end system only via learning of appropriate graph topology at each layer. In signal filtering terms, it means that our linear graph filter at each layer is always intrepretable as low-pass with known biorthogonal conditions, while the graph spectrum itself is optimized via data training. As an example application, we show that our analytical GCNN achieves image denoising performance comparable to a state-of-the-art CNN-based scheme when the training and testing data share the same statistics, and when they differ, our analytical GCNN outperforms it by more than 1dB in PSNR.

Unrolling of Deep Graph Total Variation for Image Denoising

“…In (4), a graph G with edge weights wij is assumed. As done in [13,14], in each layer we use a CNN F to compute an appropriate feature vector fi ∈ R K at runtime for each pixel i in an N -pixel patch, using which we construct a graph G. Specifically, given feature vectors fi and fj of pixels (nodes) i and j, we compute a non-negative edge weight wij between them using a Gaussian kernel, i.e.,…”

“…Progress in GSP has led to a family of graph filtering tools tailored for different imaging applications, including compression Gene Cheung acknowledges the support of the NSERC grants RGPIN-2019-06271, RGPAS-2019-00110. [10,11], denoising [12,13,14], dequantization of JPEG images [15] and deblurring [16]. Like early spatial filter work for texture recognition [17], analytically derived filters mean filter coefficients do not require learning, thus reducing the number of network parameters.…”

“…Extending these recent works on hybrid graph spectral filtering / DL architectures [13,14], in this paper we propose a fast image denoising algorithm called Deep GTV (DGTV) via unrolling of signaldependent GTV (SDGTV). Similar to [13,14], we also learn appropriate per pixel feature vectors fi to first construct a graph with few network parameters. We formulate the denoising problem using SDGTV for regularization, which promotes PWS in reconstructed signals faster than SDGLR [16].…”

“…To reduce network parameters, we turn to graph signal processing (GSP) [8,9]-the study of signals that reside on combinatorial graphs. Progress in GSP has led to a family of graph filtering tools tailored for different imaging applications, including compression [10,11], denoising [12,13,14], dequantization of JPEG images [15] and deblurring [16]. Like early spatial filter work for texture recognition [17], analytically derived filters mean filter coefficients do not require learning, thus reducing the number of network parameters.…”

Fast & Robust Image Interpolation Using Gradient Graph Laplacian Regularizer

“…In this paper, we propose a new model-based prior for image restoration that is both fast and robust. We leave the investigation of hybrid schemes that combine advantages of modelbased and data-driven approaches such as [7,8] as future work.…”