Bayesian optimal compressed sensing without priors: Parametric sure approximate message passing. Guo, C. & Davies, M. E. In *2014 22nd European Signal Processing Conference (EUSIPCO)*, pages 1347-1351, Sep., 2014.

Paper abstract bibtex

Paper abstract bibtex

It has been shown that the Bayesian optimal approximate message passing (AMP) technique achieves the minimum mean-squared error (MMSE) optimal compressed sensing (CS) recovery. However, the prerequisite of the signal prior makes it often impractical. To address this dilemma, we propose the parametric SURE-AMP algorithm. The key feature is it uses the Stein's unbiased risk estimate (SURE) based parametric family of MMSE estimator for the CS denoising. Given that the optimization of the estimator and the calculation of its mean squared error purely depend on the noisy data, there is no need of the signal prior. The weighted sum of piecewise kernel functions is used to form the parametric estimator. Numerical experiments on both Bernoulli-Gaussian and k-dense signal justify our proposal.

@InProceedings{6952469, author = {C. Guo and M. E. Davies}, booktitle = {2014 22nd European Signal Processing Conference (EUSIPCO)}, title = {Bayesian optimal compressed sensing without priors: Parametric sure approximate message passing}, year = {2014}, pages = {1347-1351}, abstract = {It has been shown that the Bayesian optimal approximate message passing (AMP) technique achieves the minimum mean-squared error (MMSE) optimal compressed sensing (CS) recovery. However, the prerequisite of the signal prior makes it often impractical. To address this dilemma, we propose the parametric SURE-AMP algorithm. The key feature is it uses the Stein's unbiased risk estimate (SURE) based parametric family of MMSE estimator for the CS denoising. Given that the optimization of the estimator and the calculation of its mean squared error purely depend on the noisy data, there is no need of the signal prior. The weighted sum of piecewise kernel functions is used to form the parametric estimator. Numerical experiments on both Bernoulli-Gaussian and k-dense signal justify our proposal.}, keywords = {Bayes methods;compressed sensing;least mean squares methods;message passing;parameter estimation;signal denoising;Bayesian optimal compressed sensing;parametric SURE approximate message passing;Bayesian optimal approximate message passing technique;minimum mean-squared error optimal compressed sensing recovery;MMSE-CS;parametric SURE-AMP algorithm;Stein unbiased risk estimate;CS denoising;MMSE estimator;noisy data;piecewise kernel functions;parametric estimator;k-dense signal;Bernoulli-Gaussian signal;signal prior;estimator optimization;Noise measurement;Noise reduction;Fasteners;Noise;Bayes methods;Optimization;Educational institutions;Compressed sensing;approximate message passing;SURE estimator;denoising}, issn = {2076-1465}, month = {Sep.}, url = {https://www.eurasip.org/proceedings/eusipco/eusipco2014/html/papers/1569924565.pdf}, }

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