HUNet: Homotopy Unfolding Network for Image Compressive Sensing

Deep Unfolding Networks (DUNs) have risen to prominence due to their interpretability and superior performance for image Compressive Sensing (CS). However, existing DUNs still face significant issues, such as the insufficient representation capability of single-scale image information during the iterative reconstruction phase and loss of feature information, which fundamentally limit the further enhancement of image CS performance. In this paper, we propose Homotopy Unfolding Network (HUNet) for image CS, which enables phase-by-phase reconstruction of images along homotopy path. Specifically, each iteration step of the traditional homotopy algorithm is mapped to a Multi-scale Homotopy Iterative Module (MHIM), which includes U-shaped stacked Window-based Transformer Blocks capable of efficient feature extraction. Within the MHIM, we design the Deep Homotopy Continuation Strategy to ensure the interpretability of the homotopy algorithm and facilitate feature learning. Additionally, we introduce a Dual-path Feature Fusion Module to mitigate the loss of high-dimensional feature information during the transmission between iterative phases, thereby maximizing the preservation of details in the reconstructed image. Extensive experiments indicate that HUNet achieves superior image reconstruction results compared to existing state-of-the-art methods.