Compressive Hyperspectral Imaging via Approximate Message Passing

Abstract

We consider a compressive hyperspectral imaging reconstruction problem, where three-dimensional spatio-spectral information about a scene is sensed by a coded aperture snapshot spectral imager (CASSI). The CASSI imaging process can be modeled as suppressing three-dimensional coded and shifted voxels and projecting these onto a two-dimensional plane, such that the number of acquired measurements is greatly reduced. On the other hand, because the measurements are highly compressive, the reconstruction process becomes challenging. We previously proposed a compressive imaging reconstruction algorithm that is applied to two-dimensional images based on the approximate message passing (AMP) framework. AMP is an iterative algorithm that can be used in signal and image reconstruction by performing denoising at each iteration. We employed an adaptive Wiener filter as the image denoiser, and called our algorithm "AMP-Wiener." In this paper, we extend AMP-Wiener to three-dimensional hyperspectral image reconstruction, and call it "AMP-3D-Wiener." Applying the AMP framework to the CASSI system is challenging, because the matrix that models the CASSI system is highly sparse, and such a matrix is not suitable to AMP and makes it difficult for AMP to converge. Therefore, we modify the adaptive Wiener filter and employ a technique called damping to solve for the divergence issue of AMP. Our approach is applied in nature, and the numerical experiments show that AMP-3D-Wiener outperforms existing widely-used algorithms such as gradient projection for sparse reconstruction (GPSR) and two-step iterative shrinkage/thresholding (TwIST) given a similar amount of runtime. Moreover, in contrast to GPSR and TwIST, AMP-3D-Wiener need not tune any parameters, which simplifies the reconstruction process.

13 pages, to appear in Journal of Selected Topics in Signal Processing

References in corpus (5)

• Compressive Hyperspectral Imaging with Side Information
• Probabilistic Reconstruction in Compressed Sensing: Algorithms, Phase Diagrams, and Threshold Achieving Matrices
• Adaptive Damping and Mean Removal for the Generalized Approximate Message Passing Algorithm
• Compressive Imaging via Approximate Message Passing with Image Denoising
• Sparse Estimation with the Swept Approximated Message-Passing Algorithm

Cited by in corpus (5)

• Mask-guided Spectral-wise Transformer for Efficient Hyperspectral Image Reconstruction
• Compressive Computed Tomography Reconstruction through Denoising Approximate Message Passing
• An Overview of Multi-Processor Approximate Message Passing
• Snapshot Hyperspectral Imaging Based on Weighted High-order Singular Value Regularization
• Analysis of Approximate Message Passing with Non-Separable Denoisers and Markov Random Field Priors