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arXiv · 1508.02454

Multi-Resolution Compressed Sensing via Approximate Message Passing

Xing Wang·Jie Liang
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Abstract

In this paper, we consider the problem of multi-resolution compressed sensing (MR-CS) reconstruction, which has received little attention in the literature. Instead of always reconstructing the signal at the original high resolution (HR), we enable the reconstruction of a low-resolution (LR) signal when there are not enough CS samples to recover a HR signal. We propose an approximate message passing (AMP)-based framework dubbed MR-AMP, and derive its state evolution, phase transition, and noise sensitivity, which show that in addition to reduced complexity, our method can recover a LR signal with bounded noise sensitivity even when the noise sensitivity of the conventional HR reconstruction is unbounded. We then apply the MR-AMP to image reconstruction using either soft-thresholding or total variation denoiser, and develop three pairs of up-/down-sampling operators in transform or spatial domain. The performance of the proposed scheme is demonstrated by both 1D synthetic data and 2D images.

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Xing Wang, Jie Liang. 2015-08-11. Multi-Resolution Compressed Sensing via Approximate Message Passing. https://arxiv.org/abs/1508.02454

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