USCTnet: A Deep Unfolding Nuclear-Norm Optimization Solver for Physically Consistent HSI Reconstruction

Reconstructing hyperspectral images (HSIs) from a single RGB image is ill-posed and can become physically inconsistent when the camera spectral sensitivity (CSS) and scene illumination are misspecified. We formulate RGB-to-HSI reconstruction as a physics-grounded inverse problem regularized by a nuclear norm in a learnable transform domain, and we explicitly estimate CSS and illumination to define the forward operator embedded in each iteration, ensuring colorimetric consistency. To avoid the cost and instability of full singular-value decompositions (SVDs) required by singular-value thresholding (SVT), we introduce a data adaptive low-rank subspace SVT operator. Building on these components, we develop USCTNet, a deep unfolding solver tailored to HSI that couples a parameter estimation module with learnable proximal updates. Extensive experiments on standard benchmarks show consistent improvements over state-of-the-art RGB-based methods in reconstruction accuracy.