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Wavelet-Based Compressed Sensing Using a Gaussian Scale Mixture Model

机译:高斯尺度混合模型的基于小波的压缩感知

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While initial compressed sensing (CS) recovery techniques operated under the implicit assumption that the sparse domain coefficients are independently distributed, recent results have indicated that integrating a statistical or structural dependence model of sparse domain coefficients into CS enhances recovery. In this paper, we present a method for exploiting empirical dependences among wavelet coefficients during CS recovery using a Bayes least-square Gaussian-scale-mixture model. The proposed model is successfully incorporated into several recent CS algorithms, including reweighted $l_{1}$ minimization (RL1), iteratively reweighted least squares, and iterative hard thresholding. Extensive experiments including comparisons with a state-of-the-art model-based CS method demonstrate that the proposed algorithms are highly effective at reducing reconstruction error and/or the number of measurements required for a desired reconstruction quality.
机译:虽然初始压缩感知(CS)恢复技术是在稀疏域系数独立分布的隐含假设下运行的,但最近的结果表明,将稀疏域系数的统计或结构相关性模型集成到CS中可以增强恢复。在本文中,我们提出了一种利用贝叶斯最小二乘高斯尺度混合模型利用CS恢复过程中小波系数之间的经验依赖性的方法。所提出的模型已成功地合并到几种最新的CS算法中,包括重新加权的l {1} $最小化(RL1),迭代重新加权的最小二乘和迭代硬阈值。广泛的实验(包括与基于最新模型的CS方法进行的比较)表明,所提出的算法在减少重建误差和/或所需重建质量所需的测量次数方面非常有效。

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