Compressed Sensing With Upscaled Vector Approximate Message Passing

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 ill-conditioned operators. Yet, its applicability limited relatively small problem sizes due the necessity compute expensive LMMSE estimator each iteration. In this work we consider of upscaling utilizing Conjugate Gradient (CG) approximate intractable estimator. We propose rigorous method for correcting tuning CG withing CG-VAMP achieve stable efficient reconstruction. To further improve performance CG-VAMP, design warm-starting scheme develop theoretical models Onsager correction State Evolution Warm-Started (WS-CG-VAMP). Additionally, robust accurate methods implementing WS-CG-VAMP algorithm. numerical experiments on large-scale image problems demonstrate that requires much fewer iterations compared same or superior level