Multi-resolution compressed sensing reconstruction via approximate message passing

We consider multi-resolution (MR) compressed sensing reconstruction, where instead of always reconstructing the signal at the original high resolution (HR), we enable the reconstruction of a better-quality low-resolution (LR) signal when the sampling rate is too low. We propose an approximate message passing (AMP)-based solution (MR-AMP). Theoretical analyses show that in addition to reduced complexity, our method can produce a LR signal with bounded mean squared error (MSE) even when the MSE of the conventional HR reconstruction is unbounded. The performance of the proposed scheme is verified using both synthetic data and natural images.