From Denoising to Compressed Sensing

A denoising algorithm seeks to remove noise, errors, or perturbations from a signal. Extensive research has been devoted to this arena over the last several decades, and as a result, todays denoisers can effectively remove large amounts of additive white Gaussian noise. A compressed sensing (CS) rec...

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Bibliographic Details
Published in:	IEEE transactions on information theory Vol. 62; no. 9; pp. 5117 - 5144
Main Authors:	Metzler, Christopher A., Maleki, Arian, Baraniuk, Richard G.
Format:	Journal Article
Language:	English
Published:	New York IEEE 01.09.2016 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Algorithm design and analysis Algorithms approximate message passing Approximation Approximation algorithms Compressed sensing denoiser Detection Electronics Error correction & detection Gaussian Iterative methods Message passing Noise Noise control Noise reduction Normal distribution Onsager correction Perturbation methods Reconstruction Reconstruction algorithms Signal processing Signal processing algorithms
ISSN:	0018-9448, 1557-9654
Online Access:	Get full text
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Abstract	A denoising algorithm seeks to remove noise, errors, or perturbations from a signal. Extensive research has been devoted to this arena over the last several decades, and as a result, todays denoisers can effectively remove large amounts of additive white Gaussian noise. A compressed sensing (CS) reconstruction algorithm seeks to recover a structured signal acquired using a small number of randomized measurements. Typical CS reconstruction algorithms can be cast as iteratively estimating a signal from a perturbed observation. This paper answers a natural question: How can one effectively employ a generic denoiser in a CS reconstruction algorithm? In response, we develop an extension of the approximate message passing (AMP) framework, called denoising-based AMP (D-AMP), that can integrate a wide class of denoisers within its iterations. We demonstrate that, when used with a high-performance denoiser for natural images, D-AMP offers the state-of-the-art CS recovery performance while operating tens of times faster than competing methods. We explain the exceptional performance of D-AMP by analyzing some of its theoretical features. A key element in D-AMP is the use of an appropriate Onsager correction term in its iterations, which coerces the signal perturbation at each iteration to be very close to the white Gaussian noise that denoisers are typically designed to remove.
AbstractList	A denoising algorithm seeks to remove noise, errors, or perturbations from a signal. Extensive research has been devoted to this arena over the last several decades, and as a result, todays denoisers can effectively remove large amounts of additive white Gaussian noise. A compressed sensing (CS) reconstruction algorithm seeks to recover a structured signal acquired using a small number of randomized measurements. Typical CS reconstruction algorithms can be cast as iteratively estimating a signal from a perturbed observation. This paper answers a natural question: How can one effectively employ a generic denoiser in a CS reconstruction algorithm? In response, we develop an extension of the approximate message passing (AMP) framework, called denoising-based AMP (D-AMP), that can integrate a wide class of denoisers within its iterations. We demonstrate that, when used with a high-performance denoiser for natural images, D-AMP offers the state-of-the-art CS recovery performance while operating tens of times faster than competing methods. We explain the exceptional performance of D-AMP by analyzing some of its theoretical features. A key element in D-AMP is the use of an appropriate Onsager correction term in its iterations, which coerces the signal perturbation at each iteration to be very close to the white Gaussian noise that denoisers are typically designed to remove.
Author	Maleki, Arian Baraniuk, Richard G. Metzler, Christopher A.
Author_xml	– sequence: 1 givenname: Christopher A. surname: Metzler fullname: Metzler, Christopher A. email: chris.metzler@rice.edu organization: Dept. of Electr. & Comput. Eng., Rice Univ., Houston, TX, USA – sequence: 2 givenname: Arian surname: Maleki fullname: Maleki, Arian email: arian@stat.columbia.edu organization: Dept. of Stat., Columbia Univ. in the City of New York, New York, NY, USA – sequence: 3 givenname: Richard G. surname: Baraniuk fullname: Baraniuk, Richard G. email: richb@rice.edu organization: Dept. of Electr. & Comput. Eng., Rice Univ., Houston, TX, USA
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Snippet	A denoising algorithm seeks to remove noise, errors, or perturbations from a signal. Extensive research has been devoted to this arena over the last several...
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SubjectTerms	Algorithm design and analysis Algorithms approximate message passing Approximation Approximation algorithms Compressed sensing denoiser Detection Electronics Error correction & detection Gaussian Iterative methods Message passing Noise Noise control Noise reduction Normal distribution Onsager correction Perturbation methods Reconstruction Reconstruction algorithms Signal processing Signal processing algorithms
Title	From Denoising to Compressed Sensing
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