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A generalized framework for learning and recovery of structured sparse signals

Justin Ziniel, Sundeep Rangan, Philip Schniter
2012 2012 IEEE Statistical Signal Processing Workshop (SSP)  
Message passing-based inference and empirical Bayesian parameter learning form the backbone of the recovery procedure.  ...  Index Terms-compressed sensing, structured sparse signal recovery, multiple measurement vectors, structured sparsity, dynamic compressed sensing  ...  While implementing a conventional BP algorithm would be computationally intractable for the factor graph of Fig. 1 , there exists an attractive approximate message passing algorithm known as GAMP [8]  ... 
doi:10.1109/ssp.2012.6319694 dblp:conf/ssp/ZinielRS12 fatcat:2xk2ixy3rvbklj7ewqvljob6bm

Invertible generative models for inverse problems: mitigating representation error and dataset bias [article]

Muhammad Asim, Max Daniels, Oscar Leong, Ali Ahmed, Paul Hand
2020 arXiv   pre-print
We additionally compare performance for compressive sensing to unlearned methods, such as the deep decoder, and we establish theoretical bounds on expected recovery error in the case of a linear invertible  ...  For compressive sensing, invertible priors can yield higher accuracy than sparsity priors across almost all undersampling ratios, and due to their lack of representation error, invertible priors can yield  ...  For compressive sensing, we use K = 18 and L = 4 for 64px recovery and K = 32, L = 6 for 128px recovery.  ... 
arXiv:1905.11672v4 fatcat:hgpfoh6frfa4thyxvhmqjzqomi

Signal recovery using expectation consistent approximation for linear observations [article]

Yoshiyuki Kabashima, Mikko Vehkapera
2014 arXiv   pre-print
A signal recovery scheme is developed for linear observation systems based on expectation consistent (EC) mean field approximation.  ...  This is numerically confirmed by experiments for the Bayesian optimal signal recovery of compressed sensing using random row-orthogonal matrices.  ...  EXPECTATION CONSISTENT SIGNAL RECOVERY A. Gibbs free energy formalism The following theorem constitutes the basis of our approximation.  ... 
arXiv:1401.5151v2 fatcat:55cilrx3jve7jmgmpafkpwojfa

On Hyperspectral Classification in the Compressed Domain [article]

Mohammad Aghagolzadeh, Hayder Radha
2015 arXiv   pre-print
A clear advantage of classification in the compressed domain is its suitability for real-time on-site processing of the sensed data.  ...  In this paper, we study the problem of hyperspectral pixel classification based on the recently proposed architectures for compressive whisk-broom hyperspectral imagers without the need to reconstruct  ...  The inferred class label for x j is sign(x T j w − b) that depends on the classifier w ∈ R d and the bias term b ∈ R.  ... 
arXiv:1508.00282v1 fatcat:ftmovoznfngrhgv4zzirkjbl74

Dynamical functional theory for compressed sensing

Burak Cakmak, Manfred Opper, Ole Winther, Bernard H. Fleury
2017 2017 IEEE International Symposium on Information Theory (ISIT)  
We introduce a theoretical approach for designing generalizations of the approximate message passing (AMP) algorithm for compressed sensing which are valid for large observation matrices that are drawn  ...  The asymptotic statistics of these fields are consistent with the replica ansatz of the compressed sensing problem.  ...  Recently, [26, 27] have reported important results on the dynamical analysis of expectation-propagation based algorithms whose fixed points are consistent with the TAP equations (9).  ... 
doi:10.1109/isit.2017.8006908 dblp:conf/isit/CakmakOWF17 fatcat:qylfv3fqr5eo5hfpb2tn3pyhii

Compressive Radar Imaging

Richard Baraniuk, Philippe Steeghs
2007 Radar Conference, IEEE  
We introduce a new approach to radar imaging based on the concept of compressive sensing (CS).  ...  These ideas could enable the design of new, simplified radar systems, shifting the emphasis from expensive receiver hardware to smart signal recovery algorithms.  ...  Acknowledgements: This work was supported by the grants DARPA/ONR N66001-06-1-2011 and N00014-06-1-0610, NSF CCF-0431150, ONR N00014-06-1-0769 and N00014-06-1-0829, AFOSR FA9550-04-1-0148, and the Texas  ... 
doi:10.1109/radar.2007.374203 fatcat:k4facdmavzbrrprrxl5wivkpc4

Sampling and Recovery of Pulse Streams

Chinmay Hegde, Richard G. Baraniuk
2011 IEEE Transactions on Signal Processing  
Third, we develop an efficient signal recovery algorithm that infers both the shape of the impulse response as well as the locations and amplitudes of the pulses.  ...  Compressive Sensing (CS) is a new technique for the efficient acquisition of signals, images, and other data that have a sparse representation in some basis, frame, or dictionary.  ...  Recovery of Pulse Streams The final ingredient in our extended CS framework for pulse streams consists of new algorithms for the stable recovery of the signals of interest from compressive measurements  ... 
doi:10.1109/tsp.2010.2103067 fatcat:6kglc6shpfdrhhorsk5ikkkptm

Dynamical Functional Theory for Compressed Sensing [article]

Burak Çakmak, Manfred Opper, Ole Winther, Bernard H. Fleury
2017 arXiv   pre-print
We introduce a theoretical approach for designing generalizations of the approximate message passing (AMP) algorithm for compressed sensing which are valid for large observation matrices that are drawn  ...  The asymptotic statistics of these fields are consistent with the replica ansatz of the compressed sensing problem.  ...  Recently, [26] , [27] have reported important results on the dynamical analysis of expectation-propagation based algorithms whose fixed points are consistent with the TAP equations (9) .  ... 
arXiv:1705.04284v1 fatcat:l7ce7rfjezhgzfz7gkglniilfy

A Coding Theory Approach to Noisy Compressive Sensing Using Low Density Frames

Mehmet Akcakaya, Jinsoo Park, Vahid Tarokh
2011 IEEE Transactions on Signal Processing  
We consider the compressive sensing of a sparse or compressible signal .  ...  Simulation results are provided, demonstrating that our approach outperforms state-of-the-art recovery algorithms for numerous cases of interest.  ...  For completeness, we also note the recent work on belief-propagation-based algorithms for compressive sensing using dense measurement matrices [21] , [33] . B.  ... 
doi:10.1109/tsp.2011.2163402 fatcat:yggjofdnwfgqbkjsxbkxzyw25i

2021 Index IEEE Transactions on Signal Processing Vol. 69

2021 IEEE Transactions on Signal Processing  
The Author Index contains the primary entry for each item, listed under the first author's name.  ...  The primary entry includes the coauthors' names, the title of the paper or other item, and its location, specified by the publication abbreviation, year, month, and inclusive pagination.  ...  ., +, TSP 2021 119-135 Phase Retrieval Using Expectation Consistent Signal Recovery Algorithm Based on Hypernetwork.  ... 
doi:10.1109/tsp.2022.3162899 fatcat:kcubj566gzb4zkj7xb5r5we3ri

Expectation-Maximization Gaussian-Mixture Approximate Message Passing

Jeremy P. Vila, Philip Schniter
2013 IEEE Transactions on Signal Processing  
When recovering a sparse signal from noisy compressive linear measurements, the distribution of the signal's non-zero coefficients can have a profound effect on recovery mean-squared error (MSE).  ...  If this distribution was apriori known, then one could use computationally efficient approximate message passing (AMP) techniques for nearly minimum MSE (MMSE) recovery.  ...  With these considerations in mind, we proposed an empirical Bayesian approach to compressive signal recovery that merges two powerful inference frameworks: expectation maximization (EM) and approximate  ... 
doi:10.1109/tsp.2013.2272287 fatcat:jogdlk7cfvghvmkpkpqksz4glu

Expectation-maximization Gaussian-mixture approximate message passing

Jeremy Vila, Philip Schniter
2012 2012 46th Annual Conference on Information Sciences and Systems (CISS)  
When recovering a sparse signal from noisy compressive linear measurements, the distribution of the signal's non-zero coefficients can have a profound effect on recovery mean-squared error (MSE).  ...  If this distribution was a priori known, then one could use computationally efficient approximate message passing (AMP) techniques for nearly minimum MSE (MMSE) recovery.  ...  With these considerations in mind, we proposed an empirical Bayesian approach to compressive signal recovery that merges two powerful inference frameworks: expectation maximization (EM) and approximate  ... 
doi:10.1109/ciss.2012.6310932 dblp:conf/ciss/VilaS12 fatcat:e4p3wdwukrd75n5jritr77irtm

Compressive Spectrum Sensing for Cognitive Radio Networks [article]

Fatima Salahdine
2018 arXiv   pre-print
One of the main challenges of cognitive radio is the wideband spectrum sensing. Existing spectrum sensing techniques are based on a set of observations sampled by an ADC at the Nyquist rate.  ...  In the deciding process, sensing results are analyzed and decisions are made based on these results.  ...  For the recovery, each compressive sensing framework has a number of recovery algorithms with different performance.  ... 
arXiv:1802.03674v1 fatcat:6ddexxzymjfqzpcw6cfoia42xy

Signal sparsity estimation from compressive noisy projections via γ-sparsified random matrices

C. Ravazzi, S. M. Fosson, T. Bianchi, E. Magli
2016 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
We demonstrate that the above model is accurate in the large system limit for a proper choice of the sensing matrix sparsifying parameter.  ...  Due to the complexity of the exact mixture model, we introduce an approximate two-component Gaussian mixture model whose parameters can be estimated via expectation-maximization techniques.  ...  INTRODUCTION Compressed Sensing (CS) [1, 2] is a novel signal acquisition technique based on the recovery of an unknown signal from a small set of linear measurements.  ... 
doi:10.1109/icassp.2016.7472434 dblp:conf/icassp/RavazziFBM16 fatcat:szg57juuy5f7fitejy5jxwtl7a

Blind Calibration in Compressed Sensing using Message Passing Algorithms [article]

Christophe Schülke, Francesco Caltagirone, Florent Krzakala, Lenka Zdeborová
2013 arXiv   pre-print
Compressed sensing (CS) is a concept that allows to acquire compressible signals with a small number of measurements. As such it is very attractive for hardware implementations.  ...  We extend the approximate message passing (AMP) algorithm used in CS to the case of blind calibration.  ...  The Calibration-AMP algorithm The approximate message passing algorithm is based on a Bayesian probabilistic formulation of the reconstruction problem.  ... 
arXiv:1306.4355v1 fatcat:7r2zl77rvbfu7o6nx2xt3gp4ba
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