Hierarchical Spatial-Frequency Aggregation for Spectral Deconvolution Imaging

Abstract: Computational spectral imaging (CSI) achieves real-time hyperspectral imaging through co-designed optics and algorithms, but typical CSI methods suffer from a bulky footprint and limited fidelity. Therefore, Spectral Deconvolution imaging (SDI) methods based on PSF engineering have been proposed to achieve high-fidelity compact CSI design recently. However, the composite convolution-integration operations of SDI render the normal-equation coefficient matrix scene-dependent, which hampers the efficient exploitation of imaging priors and poses challenges for accurate reconstruction. To tackle the inherent data-dependent operators in SDI, we introduce a Hierarchical Spatial-Spectral Aggregation Unfolding Framework (HSFAUF). By decomposing subproblems and projecting them into the frequency domain, HSFAUF transforms nonlinear processes into linear mappings, thereby enabling efficient solutions. Furthermore, to integrate spatial-spectral priors during iterative refinement, we propose a Spatial-Frequency Aggregation Transformer (SFAT), which explicitly aggregates information across spatial and frequency domains. By integrating SFAT into HSFAUF, we develop a Transformer-based deep unfolding method, \textbf{H}ierarchical \textbf{S}patial-\textbf{F}requency \textbf{A}ggregation \textbf{U}nfolding \textbf{T}ransformer (HSFAUT), to solve the inverse problem of SDI. Systematic simulated and real experiments show that HSFAUT surpasses SOTA methods with cheaper memory and computational costs, while exhibiting optimal performance on different SDI systems.