Versatile Denoising-Based Approximate Message Passing for Compressive Sensing

Approximate message passing-based compressive sensing reconstruction has received increasing attention, the performance of which depends heavily on the ability of the denoising operator. However, most methods only employ an off-the-shelf denoising model as the denoising operator of the iteration solver, which imposes an unfavorable limit on reconstruction performance of compressive sensing. To solve the aforementioned issue, we propose a novel versatile denoising-based approximate message passing model, abbreviated as VD-AMP, for compressive sensing (CS) recovery. To be specific, we meticulously design a double encoder-decoder denoising network (DEDNet), which manifests the impressive performance in Gaussian denoising. Moreover, a fine-grained noise level division (FNLD) solution is proposed to release the potential of the well-designed DEDNet so as to improve the reconstruction performance. However, strengthening the denoiser alone fails to remove the distortion artifact of reconstruction images at low sampling rates. To alleviate the defect, we propose an anti-aliasing sampling (AS), which firstly maps the input image to a smoothing sub-space using the proposed DEDNet before vanilla sampling, reducing aliasing between high-frequency and low-frequency information on measurement. Extensive experiments on benchmark datasets demonstrate that the proposed VD-AMP significantly outperforms state-of-the-art CS reconstruction models by a large margin, e.g., up to 2 dB gains on PSNR.