Paper Info
Title
Near Optimal Compressed Sensing Without Priors: Parametric SURE Approximate Message Passing
Abstract
Both theoretical analysis and empirical evidence confirm that the approximate message passing (AMP) algorithm can be interpreted as recursively solving a signal denoising problem: at each AMP iteration, one observes a Gaussian noise perturbed original signal. Retrieving the signal amounts to a successive noise cancellation until the noise variance decreases to a satisfactory level. In this paper, we incorporate the Stein's unbiased risk estimate (SURE) based parametric denoiser with the AMP framework and propose the novel parametric SURE-AMP algorithm. At each parametric SURE-AMP iteration, the denoiser is adaptively optimized within the parametric class by minimizing SURE, which depends purely on the noisy observation. In this manner, the parametric SURE-AMP is guaranteed with the best-in-class recovery and convergence rate. If the parametric family includes the families of the mimimum mean squared error (MMSE) estimators, we are able to achieve the Bayesian optimal AMP performance without knowing the signal prior. In the paper, we resort to the linear parameterization of the SURE based denoiser and propose three different kernel families as the base functions. Numerical simulations with the Bernoulli-Gaussian, k-dense and Student's-t signals demonstrate that the parametric SURE-AMP does not only achieve the state-of-the-art recovery but also runs more than 20 times faster than the EM-GM-GAMP algorithm. Natural image simulations confirm the advantages of the parametric SURE-AMP for signals without prior information.
Year
DOI
Venue
2015
10.1109/TSP.2015.2408569
Signal Processing, IEEE Transactions  
Keywords
DocType
Volume
parametric sure approximate message passing,signal denoising,student's-t signal demonstrate,bayesian optimal amp performance,stein unbiased risk estimate based parametric denoiser,mmse estimator,bayes methods,parametric estimator,linear parameterization,signal retrieval,approximate message passing algorithm,natural image simulation,image denoising,stein's unbiased risk estimate,least mean squares methods,compressed sensing,successive noise cancellation,sure-amp iteration,image retrieval,gaussian noise perturbed original signal,mimimum mean squared error estimator,bernoulli-gaussian,gaussian noise,message passing,noise measurement,stein s unbiased risk estimate,kernel,estimation,algorithm design and analysis,noise reduction,noise
Journal
63
Issue
ISSN
Citations 
8
1053-587X
15
PageRank 
References 
Authors
0.69
21
2
Name
Order
Citations
PageRank
Chunli Guo1263.82
Mike E. Davies21664120.39