论文标题
通过高尺度向量近似消息传递的压缩感测
Compressed Sensing with Upscaled Vector Approximate Message Passing
论文作者
论文摘要
最近提出的矢量近似消息传递（VAMP）算法在求解相关的线性逆问题方面表现出了巨大的重建潜力。 VAMP提供了较高的触电改进，可以利用BM3D等强大的DeNoiser，它具有严格定义的动力学，并且能够恢复通过高度不强调且条件不足的线性操作员测量的信号。但是，由于必要计算每次迭代时昂贵的LMMSE估计器，因此其适用性仅限于相对较小的问题尺寸。在这项工作中，我们考虑了通过利用共轭梯度（CG）近似棘手的LMMSE估计量来升级VAMP的问题。我们提出了一种使用CG-VAMP校正和调整CG的严格方法，以实现稳定，有效的重建。为了进一步提高CG-VAMP的性能，我们为CG设计了一个温暖的启动方案，并开发了用于Onsager校正的理论模型和暖启动的CG-VAMP（WS-CG-VAMP）的状态演变。此外，我们开发了实现WS-CG-VAMP算法的强大而准确的方法。大规模图像重建问题上的数值实验表明，与CG-VAMP相比，WS-CG-VAMP需要更少的CG迭代才能实现相同或优质的重建水平。
The Recently proposed Vector Approximate Message Passing (VAMP) algorithm demonstrates a great reconstruction potential at solving compressed sensing related linear inverse problems. VAMP provides high per-iteration improvement, can utilize powerful denoisers like BM3D, has rigorously defined dynamics and is able to recover signals measured by highly undersampled and ill-conditioned linear operators. Yet, its applicability is limited to relatively small problem sizes due to the necessity to compute the expensive LMMSE estimator at each iteration. In this work we consider the problem of upscaling VAMP by utilizing Conjugate Gradient (CG) to approximate the intractable LMMSE estimator. We propose a rigorous method for correcting and tuning CG withing CG-VAMP to achieve a stable and efficient reconstruction. To further improve the performance of CG-VAMP, we design a warm-starting scheme for CG and develop theoretical models for the Onsager correction and the State Evolution of Warm-Started CG-VAMP (WS-CG-VAMP). Additionally, we develop robust and accurate methods for implementing the WS-CG-VAMP algorithm. The numerical experiments on large-scale image reconstruction problems demonstrate that WS-CG-VAMP requires much fewer CG iterations compared to CG-VAMP to achieve the same or superior level of reconstruction.
