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Filtered gradient reconstruction algorithm for compressive spectral imaging

机译：压缩梯度成像的滤波梯度重构算法

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摘要

Compressive sensing matrices are traditionally based on random Gaussian and Bernoulli entries. Nevertheless, they are subject to physical constraints, and their structure unusually follows a dense matrix distribution, such as the case of the matrix related to compressive spectral imaging (CSI). The CSI matrix represents the integration of coded and shifted versions of the spectral bands. A spectral image can be recovered from CSI measurements by using iterative algorithms for linear inverse problems that minimize an objective function including a quadratic error term combined with a sparsity regularization term. However, current algorithms are slow because they do not exploit the structure and sparse characteristics of the CSI matrices. A gradient-based CSI reconstruction algorithm, which introduces a filtering step in each iteration of a conventional CSI reconstruction algorithm that yields improved image quality, is proposed. Motivated by the structure of the CSI matrix, Φ, this algorithm modifies the iterative solution such that it is forced to converge to a filtered version of the residual Φ~r y, where y is the compressive measurement vector. We show that the filtered-based algorithm converges to better quality performance results than the unfiltered version. Simulation results highlight the relative performance gain over the existing iterative algorithms.
机译：传统上，压缩感测矩阵基于随机高斯和伯努利项。然而，它们受到物理约束，并且其结构异常地遵循密集的矩阵分布，例如与压缩光谱成像（CSI）有关的矩阵的情况。 CSI矩阵表示频谱带的编码版本和移位版本的集成。通过使用线性反问题的迭代算法可以从CSI测量中恢复光谱图像，该算法将包含二次误差项和稀疏正则项的目标函数最小化。但是，当前的算法很慢，因为它们没有利用CSI矩阵的结构和稀疏特征。提出了一种基于梯度的CSI重建算法，该算法在常规CSI重建算法的每次迭代中引入了滤波步骤，从而提高了图像质量。受CSI矩阵Φ的激励，该算法修改了迭代解，以使其被迫收敛到残差Φy y的滤波版本，其中y是压缩测量向量。我们表明，基于过滤的算法比未过滤的算法收敛到更好的质量性能结果。仿真结果突出了相对于现有迭代算法的相对性能提升。

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