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.Comment: 13 pages, to appear in Journal of Selected Topics in Signal Processin

An overview of multi-processor approximate message passing

“…where the goal is to estimate the unknown x ∈ R N given the matrix A ∈ R M ×N and statistical information about the signal x and the noise w ∈ R M . These problems have received significant attention in the compressed sensing literature [1,2] with applications to image reconstruction [3], communication systems [4], and machine learning problems [5]. In recent years, many applications have seen explosive growth in the sizes of data sets.…”

“…In recent years, many applications have seen explosive growth in the sizes of data sets. Some linear inverse problems, for example in hyper spectral image reconstruction [3,6,7], are so large that the M × N matrix elements cannot be stored on conventional computing systems. To solve these largescale problems, it is possible to partition the matrix A among multiple computing nodes in multi-processor (MP) systems.…”

“…where A p ∈ R M ×Np is the sub-matrix that is stored in processor p, and P p=1 N p = N . Many studies on solving the column-wise partitioned linear inverse problem (3) have been in the context of distributed feature selection. For example, Zhou et al [17] modeled feature selection as a parallel group testing problem.…”

Analysis of Approximate Message Passing With Non-Separable Denoisers and Markov Random Field Priors

“…We now use the Bayesian sliding-window denoiser defined in (17) to reconstruct binary texture images shown in Figure 5. The MRF prior is the same type as described in Section 2.3.1, namely the Π + Binary MRF, but we set the parameters {p = 0.18, q = 0.16, r = 0.034, s = 0.01}.…”

3D compressive spectral integral imaging

“…where A = HT represents the sensing matrix of the proposed system. To solve this underdetermined linear system, the Two-step iterative shrinkage/thresholding (TwIST) [19] reconstruction algorithm is used although a number of other method can be used [20,21]. The signal recovery is obtained f 0 as the solution of…”