LCTC: Lightweight Convolutional Thresholding Sparse Coding Network Prior for Compressive Hyperspectral Imaging

Compressive spectral imaging has garnered significant attention for its ability to effectively enhance the captured spatial and spectral information. Predominant methods, based on compressive sensing, typically formulate the imaging task as a constrained optimization problem and rely on hand-crafted priors to model the sparsity of spectral images. However, these approaches often suffer from suboptimal performance due to the inherent difficulty of identifying an appropriate transform space where spectral images exhibit sparsity. To overcome this limitation, we propose a novel convolutional sparse coding-inspired untrained network prior for fast and adaptive identification of the sparse transform domain and compressible signal. Specifically, a Lightweight Convolutional Thresholding sparse Coding (LCTC) network is designed as the sparse transform domain, with its inputs interpreted as sparse coefficients. Crucially, both the transform domain and its coefficients are solved in a self-supervised learning manner. Furthermore, we demonstrate that LCTC prior can be seamlessly incorporated into the iterative optimization algorithm as a Plug-and-Play (PnP) regularization. Both the LCTC and PnP-LCTC exhibit superior performance compared to previous methods. Experiments under various scenarios validate the effectiveness and efficiency of our approach.