Title: Residual Pyramid Atrous Filtering Network with the Error Low-Rank Respresentation
Primary area: applications to computer vision, audio, language, and other modalities
Keywords: non-convex optimization, image filtering, deep learning

Abstract: Image filtering aims to eliminate perturbations and textures while preserving dominant structures, serving a pivotal role in various image processing tasks. More recently, significant advances in filtering techniques have been developed. However, existing approaches typically suffer from oversmoothing edges, gradient reversal, and halos. Such issues originate from the difficulty in striking an optimal trade-off between filtering multi-scale textures and preserving edges. Furthermore, deep learning-based filtering frameworks lack modules designed to capture features of different long-range dependence textures. Consequently, the task of filtering textures while maintaining edge integrity remains a significant challenge. To address these issues, we propose a novel residual pyramid atrous filtering network (RPAFNet) that utilizes the error low-rank representation. Specifically, we introduce a lightweight dilated spatial convolution (LDSC) module for effectively extracting multi-scale texture features. To boost the reconstruction feature space, we propose a difference residual layer (DRL) module for connecting the encoder and decoder. Additionally, by employing low-rank approximation, we introduce a new non-convex optimization model, termed gradient error low-rank representation model (GELR), which effectively suppresses textures and preserves edges. This paper provides complete theoretical derivations for solving GELR and its convergence. Extensive experiments demonstrate that the proposed approach outperforms previous techniques in attaining an equilibrium between texture filtering and edge retention, as validated by both visual comparison and quantitative evaluation across various smoothing and downstream applications.