[Paper Review] A Fast Alternating Minimization Algorithm for Coded Aperture Snapshot Spectral Imaging Based on Sparsity and Deep Image Priors

Qile Zhao, Xianhong Zhao+3 more|arXiv (Cornell University)|Jun 12, 2022

Sparse and Compressive Sensing Techniques4 citations

TL;DR

This paper proposes Fama-SDIP, a fast alternating minimization algorithm for coded aperture snapshot spectral imaging (CASSI) that leverages sparsity and deep image priors (DIP) to reconstruct hyperspectral images (HSIs) without requiring any training data. By integrating DIP into compressive sensing via a split Bregman framework, the method achieves state-of-the-art reconstruction quality in under 11 minutes, significantly outperforming existing unsupervised and supervised methods in both simulation and real-world experiments.

ABSTRACT

Coded aperture snapshot spectral imaging (CASSI) is a technique used to reconstruct three-dimensional hyperspectral images (HSIs) from one or several two-dimensional projection measurements. However, fewer projection measurements or more spectral channels leads to a severly ill-posed problem, in which case regularization methods have to be applied. In order to significantly improve the accuracy of reconstruction, this paper proposes a fast alternating minimization algorithm based on the sparsity and deep image priors (Fama-SDIP) of natural images. By integrating deep image prior (DIP) into the principle of compressive sensing (CS) reconstruction, the proposed algorithm can achieve state-of-the-art results without any training dataset. Extensive experiments show that Fama-SDIP method significantly outperforms prevailing leading methods on simulation and real HSI datasets.

Motivation & Objective

• To address the ill-posed nature of CASSI reconstruction when few measurements or high spectral channels are used.
• To develop a reconstruction algorithm that does not require large-scale training datasets, overcoming limitations of supervised deep learning methods.
• To improve reconstruction accuracy and speed by synergistically combining sparsity prior and deep image prior (DIP).
• To achieve state-of-the-art performance in both simulation and real-world CASSI experiments using a single, unified framework.

Proposed method

• The method formulates CASSI reconstruction as a constrained optimization problem using compressive sensing principles with sparsity and DIP regularization.
• It employs a split Bregman algorithm to alternately minimize the data-fidelity term and enforce sparsity and DIP constraints.
• The deep image prior is implemented via a generative neural network that implicitly learns image priors through optimization, not training.
• Sparsity is enforced via a 3D total variation (TV) norm on the hyperspectral cube to preserve edges and reduce noise.
• The algorithm uses a warm start from a sparsity-based reconstruction to accelerate convergence.
• The alternating minimization scheme alternates between updating the HSI estimate and the auxiliary variables in the split Bregman framework.

Experimental results

Research questions

• RQ1 Can a training-free method combining sparsity and deep image priors achieve superior HSI reconstruction performance in CASSI?
• RQ2 How does the proposed Fama-SDIP algorithm compare to supervised and unsupervised baselines in terms of reconstruction quality and speed?
• RQ3 Can the integration of DIP and sparsity priors effectively regularize the ill-posed CASSI inverse problem without requiring labeled data?
• RQ4 Does the method maintain high spectral accuracy and spatial detail under low-signal conditions or real-world measurement noise?

Key findings

• Fama-SDIP achieves state-of-the-art performance on both simulated and real CASSI datasets, significantly outperforming GPSR, TwIST, GAP-TV, PnP-DIP, and DGSMP in PSNR and SSIM.
• On real data with 18 spectral channels and 512×512 spatial resolution, Fama-SDIP produces sharper edges and fewer artifacts than all compared methods.
• The method reconstructs HSIs in just 10.75 minutes, offering over 10× speedup compared to PnP-DIP (115.63 min) while delivering better results.
• Fama-SDIP achieves higher spectral correlation (r > 0.98) with reference spectra across selected regions, indicating superior spectral fidelity.
• The algorithm demonstrates robustness in real-world conditions, outperforming PnP-HSI, which underperforms even GAP-TV due to domain shift in real data.
• The use of a sparsity-based warm start enables faster convergence and improved stability in the alternating minimization process.