LRDUN: A Low-Rank Deep Unfolding Network for Efficient Spectral Compressive Imaging

TL;DR

This work tackles the ill-posed and computation-heavy problem of reconstructing hyperspectral images from compressed 2D measurements in SCI systems. It reformulates the problem by enforcing a low-rank decomposition $\mathcal{X}=\mathcal{A}\times_3\mathbf{E}$, leading to two reduced sensing models $\mathbf{y}=\boldsymbol{\Phi}_{\mathbf{A}}\mathbf{e}+\mathbf{n}$ and $\mathbf{y}=\boldsymbol{\Phi}_{\mathbf{E}}\mathbf{a}+\mathbf{n}$ with $k\ll B$. Building on this, the Low-Rank Deep Unfolding Network (LRDUN) solves the two subproblems within an unfolded proximal gradient descent framework and introduces Generalized Feature Unfolding Mechanism (GFUM) to decouple the physical rank from the feature dimensionality, enhancing representational capacity. Extensive experiments on simulated and real data show state-of-the-art reconstruction quality with significantly reduced computational cost, demonstrating the practical value of physics-informed, efficient SCI reconstruction through LR-based modeling.

Abstract

Deep unfolding networks (DUNs) have achieved remarkable success and become the mainstream paradigm for spectral compressive imaging (SCI) reconstruction. Existing DUNs are derived from full-HSI imaging models, where each stage operates directly on the high-dimensional HSI, refining the entire data cube based on the single 2D coded measurement. However, this paradigm leads to computational redundancy and suffers from the ill-posed nature of mapping 2D residuals back to 3D space of HSI. In this paper, we propose two novel imaging models corresponding to the spectral basis and subspace image by explicitly integrating low-rank (LR) decomposition with the sensing model. Compared to recovering the full HSI, estimating these compact low-dimensional components significantly mitigates the ill-posedness. Building upon these novel models, we develop the Low-Rank Deep Unfolding Network (LRDUN), which jointly solves the two subproblems within an unfolded proximal gradient descent (PGD) framework. Furthermore, we introduce a Generalized Feature Unfolding Mechanism (GFUM) that decouples the physical rank in the data-fidelity term from the feature dimensionality in the prior module, enhancing the representational capacity and flexibility of the network. Extensive experiments on simulated and real datasets demonstrate that the proposed LRDUN achieves state-of-the-art (SOTA) reconstruction quality with significantly reduced computational cost.

Figures (7)

• Figure 1: Performance (PSNR) vs. Efficiency (FLOPs). LRDUN (red) achieves a superior accuracy-efficiency trade-off, attaining competitive PSNR with significantly lower computational cost than SOTA methods.
• Figure 2: Overall architecture of LRDUN. The network unfolds an optimization into N stages. Each stage alternates between solving an E-problem (spectral basis feature) and an A-problem (subspace images feature), each comprising a data-fidelity feature term via (b) GFUM and a learnable (c) ProxyNet E or (d) ProxyNet A.
• Figure 3: The architecture of the SCAB.
• Figure 4: Reconstructed results of the simulated Scene 7, showing 4 out of 28 spectral channels obtained by state-of-the-art methods. One representative region is selected for spectral analysis.
• Figure 5: Reconstructed results of real-world Scene 4, displaying 4 out of 28 spectral channels. LRDUN-9stg (simu) denotes the model obtained directly from the Simulation Experiment.