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Abstract
DenoisingAMP (DAMP) can be viewed as an iterative algorithm where at each iteration a nonlinear denoising function is applied to the signal estimate. DAMP algorithm has been analysed in terms of inferential accuracy without considering computational complexity. This is an important missing aspect since the denoising is often the computational bottleneck in the DAMP reconstruction. The approach that it is proposed in this work is different; we aim to design a mechanism for leveraging a hierarchy denoising models (MultiDAMP) in order to minimize the overall complexity given the expected risk, i.e. the estimation error. The intuition comes from the observation that at earlier iteration, when the estimate is far according to some distance to the true signal, the algorithm does not need a complicated denoiser, since the structure of the signal is poor, but faster denoisers and this leads to the idea of defining a family/hierarchy of denoisers of increased complexity.
The main challenge is to define a switching scheme which is based on the empirical finding that in MultiDAMP we can predict exactly, in the large system limit, the evolution of the Mean Square Error. We can exploit the State Evolution, evaluated on a set of training images, to find a proper switching strategy. The proposed framework has been tested on i.i.d. random Gaussian measurements with Gaussian noise and for deconvolution problem. The results show the effectiveness of the proposed reconstruction algorithm.
The main challenge is to define a switching scheme which is based on the empirical finding that in MultiDAMP we can predict exactly, in the large system limit, the evolution of the Mean Square Error. We can exploit the State Evolution, evaluated on a set of training images, to find a proper switching strategy. The proposed framework has been tested on i.i.d. random Gaussian measurements with Gaussian noise and for deconvolution problem. The results show the effectiveness of the proposed reconstruction algorithm.
Original language  English 

Title of host publication  Proceedings of Workshop on Signal Processing with Adaptive Sparse Structured Representations 2017 
Publication status  Published  5 Jun 2017 
Event  7th Workshop on Signal Processing with Adaptive Sparse Structured Representations, 2017  Lisbon, Portugal Duration: 5 Jun 2017 → 8 Jun 2017 
Conference
Conference  7th Workshop on Signal Processing with Adaptive Sparse Structured Representations, 2017 

Country/Territory  Portugal 
City  Lisbon 
Period  5/06/17 → 8/06/17 
Keywords
 Denoising Approximate Message Passing
 Compressed sensing (CS)
 Complexity analysis
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 1 Finished

Exploiting low dimensional models in sensing, computation and signal processing
1/09/16 → 31/08/22
Project: Research