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.

翻译：最近提出的矢量近似电文传递(VAMP)算法表明,在解决压缩遥感相关线性反向问题方面具有巨大的重建潜力。 VAMP提供高水平的逐度改进,能够利用BM3D等强固固度器,具有严格定义的动态,能够恢复高压和条件差的线性操作员测量的信号。然而,由于需要在每个循环中计算昂贵的LMMSSE估计器(VAMP),其适用性仅限于相对较小的问题规模。在这项工作中,我们考虑利用CG(CG)来接近棘手的LMMSE估计器(CG)来提升VAMP(CG)的问题。我们提出了一个严格的方法来纠正和调整CG-VAMP(C),以便实现稳定和有效的重建。为了进一步改善CG-VAMP(W-C),我们设计了一个热点启动的C-G-VAMP(WS-C-G-VAMP(C-VAMP)国家演化模型(WS-G-G-VAMP)的理论模型模型模型模型模型。此外,我们为C-G-G-GSARAMAMA-S-S-S-S-SADAVA)的大规模的大规模重建,我们提出了较强力和较高级的精确和较精确的模型,为了执行高的C-G-G-G-GAVAMABAFAFAMAMAMAMA-S-G)的模型,我们化的模型,我们需要在大规模的大规模的模型,我们为C的大规模的重建,我们化的模型,我们化的模型,我们化的模型,我们为C-G-VAFAFA-S-S-S-G-G-VA-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-SAFAFA-S-SAR-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-VABA-S-S-S-S-S