Multi Denoising Approximate Message Passing for Optimal Recovery with Lower Computational Cost

Alessandro Perelli, Michael Davies

Research output: Chapter in Book/Report/Conference proceedingConference contribution


An emerging issue in large-scale inverse problems is constituted by the interdependency between computational and recovery performance; in particular in practical application, such as medical imaging, it is crucial to provide high quality estimates given bounds on computational time. While most work in this direction has gone down the lines of improving optimisation schemes, in this paper we are proposing and investigating a different approach based on a multi denoising approximate message passing (MultiD-AMP) framework for Compressive Sensing (CS) image reconstruction which exploits an hierarchy of denoisers by starting with a low fidelity model and then using the estimate as starting point for a higher fidelity models through an iterative reconstruction algorithm. MultiD-AMP achieves lower time complexity and same accuracy compared to using the same most accurate denoiser as in D-AMP. The novelty of our approach is based on exploiting the deterministic state evolution of AMP, which means the predictability of the recovery performances, to design a strategy for selecting the denoiser from a set ordered by both computational complexity and statistical efficiency. We apply the MultiD-AMP framework for image reconstruction given noisy Gaussian random linear measurements. Furthermore we extend and show the applicability of MultiD-AMP for CS to image reconstruction.
Original languageEnglish
Title of host publicationProceedings of the 25th European Signal Processing Conference (EUSIPCO)
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Publication statusPublished - 26 Oct 2017
Event 25th European Signal Processing Conference (EUSIPCO) 2017 - Kos, Greece
Duration: 28 Aug 20172 Sep 2017


Conference 25th European Signal Processing Conference (EUSIPCO) 2017
Internet address


  • Denoising Approximate Message Passing
  • Complexity Analysis
  • Image Reconstruction

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