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81
A fast algorithm for sparse reconstruction based on shrinkage, subspace optimization and continuation
 SIAM Journal on Scientific Computing
, 2010
"... Abstract. We propose a fast algorithm for solving the ℓ1regularized minimization problem minx∈R n µ‖x‖1 + ‖Ax − b ‖ 2 2 for recovering sparse solutions to an undetermined system of linear equations Ax = b. The algorithm is divided into two stages that are performed repeatedly. In the first stage a ..."
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Cited by 54 (8 self)
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Abstract. We propose a fast algorithm for solving the ℓ1regularized minimization problem minx∈R n µ‖x‖1 + ‖Ax − b ‖ 2 2 for recovering sparse solutions to an undetermined system of linear equations Ax = b. The algorithm is divided into two stages that are performed repeatedly. In the first stage a firstorder iterative method called “shrinkage ” yields an estimate of the subset of components of x likely to be nonzero in an optimal solution. Restricting the decision variables x to this subset and fixing their signs at their current values reduces the ℓ1norm ‖x‖1 to a linear function of x. The resulting subspace problem, which involves the minimization of a smaller and smooth quadratic function, is solved in the second phase. Our code FPC AS embeds this basic twostage algorithm in a continuation (homotopy) approach by assigning a decreasing sequence of values to µ. This code exhibits stateoftheart performance both in terms of its speed and its ability to recover sparse signals. It can even recover signals that are not as sparse as required by current compressive sensing theory.
Compressed sensing for realtime energyefficient ecg compression on wireless body sensor nodes
 BIOMEDICAL ENGINEERING, IEEE TRANSACTIONS ON
, 2011
"... Wireless body sensor networks (WBSN) hold the promise to be a key enabling information and communications technology for nextgeneration patientcentric telecardiology or mobile cardiology solutions. Through enabling continuous remote cardiac monitoring, they have the potential to achieve improved ..."
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Cited by 42 (4 self)
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Wireless body sensor networks (WBSN) hold the promise to be a key enabling information and communications technology for nextgeneration patientcentric telecardiology or mobile cardiology solutions. Through enabling continuous remote cardiac monitoring, they have the potential to achieve improved personalization and quality of care, increased ability of prevention and early diagnosis, and enhanced patient autonomy, mobility, and safety. However, stateoftheart WBSNenabled ECG monitors still fall short of the required functionality, miniaturization, and energy efficiency. Among others, energy efficiency can be improved through embedded ECG compression, in order to reduce airtime over energyhungry wireless links. In this paper, we quantify the potential of the emerging compressed sensing (CS) signal acquisition/compression paradigm for lowcomplexity energyefficient ECG compression on the stateoftheart Shimmer WBSN mote. Interestingly, our results show that CS represents a competitive alternative to stateoftheart digital wavelet transform (DWT)based ECG compression solutions in the context of WBSNbased ECG monitoring systems. More specifically, while expectedly exhibiting inferior compression performance than its DWTbased counterpart for a given reconstructed signal quality, its substantially lower complexity and CPU execution time enables it to ultimately outperform DWTbased ECG compression in terms of overall energy efficiency. CSbased ECG compression is accordingly shown to achieve a 37.1 % extension in node lifetime relative to its DWTbased counterpart for “good” reconstruction quality.
Analysis and generalizations of the linearized Bregman method
 SIAM J. IMAGING SCI
, 2010
"... This paper analyzes and improves the linearized Bregman method for solving the basis pursuit and related sparse optimization problems. The analysis shows that the linearized Bregman method has the exact regularization property; namely, it converges to an exact solution of the basis pursuit problem ..."
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Cited by 36 (9 self)
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This paper analyzes and improves the linearized Bregman method for solving the basis pursuit and related sparse optimization problems. The analysis shows that the linearized Bregman method has the exact regularization property; namely, it converges to an exact solution of the basis pursuit problem whenever its smooth parameter α is greater than a certain value. The analysis is based on showing that the linearized Bregman algorithm is equivalent to gradient descent applied to a certain dual formulation. This result motivates generalizations of the algorithm enabling the use of gradientbased optimization techniques such as line search, Barzilai–Borwein, limited memory BFGS (LBFGS), nonlinear conjugate gradient, and Nesterov’s methods. In the numerical simulations, the two proposed implementations, one using Barzilai–Borwein steps with nonmonotone line search and the other using LBFGS, gave more accurate solutions in much shorter times than the basic implementation of the linearized Bregman method with a socalled kicking technique.
Compressed Synthetic Aperture Radar
, 2010
"... In this paper, we introduce a new synthetic aperture radar (SAR) imaging modality which can provide a highresolution map of the spatial distribution of targets and terrain using a significantly reduced number of needed transmitted and/or received electromagnetic waveforms. This new imaging scheme, ..."
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Cited by 26 (3 self)
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In this paper, we introduce a new synthetic aperture radar (SAR) imaging modality which can provide a highresolution map of the spatial distribution of targets and terrain using a significantly reduced number of needed transmitted and/or received electromagnetic waveforms. This new imaging scheme, requires no new hardware components and allows the aperture to be compressed. It also presents many new applications and advantages which include strong resistance to countermesasures and interception, imaging much wider swaths and reduced onboard storage requirements.
Online Sparse System Identification and Signal Reconstruction using Projections onto Weighted ℓ1 Balls
 IEEE TRANSACTIONS ON SIGNAL PROCESSING
, 2010
"... This paper presents a novel projectionbased adaptive algorithm for sparse signal and system identification. The sequentially observed data are used to generate an equivalent sequence of closed convex sets, namely hyperslabs. Each hyperslab is the geometric equivalent of a cost criterion, that quant ..."
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Cited by 24 (3 self)
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This paper presents a novel projectionbased adaptive algorithm for sparse signal and system identification. The sequentially observed data are used to generate an equivalent sequence of closed convex sets, namely hyperslabs. Each hyperslab is the geometric equivalent of a cost criterion, that quantifies “data mismatch”. Sparsity is imposed by the introduction of appropriately designed weighted ℓ1 balls and the related projection operator is also derived. The algorithm develops around projections onto the sequence of the generated hyperslabs as well as the weighted ℓ1 balls. The resulting scheme exhibits linear dependence, with respect to the unknown system’s order, on the number of multiplications/additions and an O(L log2 L) dependence on sorting operations, where L is the length of the system/signal to be estimated. Numerical results are also given to validate the performance of the proposed method against the LASSO algorithm and two very recently developed adaptive sparse schemes that fuse arguments from the LMS / RLS adaptation mechanisms with those imposed by the lasso rational.
Terahertz imaging with compressed sensing and phase retrieval
, 2008
"... We describe a novel, highspeed pulsed terahertz (THz) Fourier imaging system based on compressed sensing (CS), a new signal processing theory, which allows image reconstruction with fewer samples than traditionally required. Using CS, we successfully reconstruct a 64�64 image of an object with pixe ..."
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Cited by 14 (1 self)
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We describe a novel, highspeed pulsed terahertz (THz) Fourier imaging system based on compressed sensing (CS), a new signal processing theory, which allows image reconstruction with fewer samples than traditionally required. Using CS, we successfully reconstruct a 64�64 image of an object with pixel size 1.4 mm using a randomly chosen subset of the 4096 pixels, which defines the image in the Fourier plane, and observe improved reconstruction quality when we apply phase correction. For our chosen image, only about 12 % of the pixels are required for reassembling the image. In combination with phase retrieval, our system has the capability to reconstruct images with only a small subset of Fourier amplitude measurements and thus has potential application in THz imaging with cw sources. © 2008 Optical Society of America OCIS codes: 110.6795, 320.7100. With applications to aerospace, homeland security, medical imaging, and quality control of packaged goods, timedomain terahertz (THz) imaging systems have proven valuable in numerous fields. However, these systems are generally limited by slow image acquisition rate [1]. In the fastest example of rasterscan
Design and exploration of lowpower analog to information conversion based on compressed sensing
 IN CIRCUITS SYST
, 2012
"... The longstanding analogtodigital conversion paradigm based on Shannon/Nyquist sampling has been challenged lately, mostly in situations such as radar and communication signal processing where signal bandwidth is so large that sampling architectures constraints are simply not manageable. Compresse ..."
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Cited by 10 (4 self)
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The longstanding analogtodigital conversion paradigm based on Shannon/Nyquist sampling has been challenged lately, mostly in situations such as radar and communication signal processing where signal bandwidth is so large that sampling architectures constraints are simply not manageable. Compressed sensing (CS) is a new emerging signal acquisition/compression paradigm that offers a striking alternative to traditional signal acquisition. Interestingly, by merging the sampling and compression steps, CS also removes a large part of the digital architecture and might thus considerably simplify analogtoinformation (A2I) conversion devices. This socalled “analog CS,” where compression occurs directly in the analog sensor readout electronics prior to analogtodigital conversion, could thus be of great importance for applications where bandwidth is moderate, but computationally complex, and power resources are severely constrained. In our
Exploiting SelfSimilarities for Single Frame SuperResolution
"... Abstract. We propose a superresolution method that exploits selfsimilarities and group structural information of image patches using only one single input frame. The superresolution problem is posed as learning the mapping between pairs of lowresolution and highresolution image patches. Instead ..."
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Cited by 9 (1 self)
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Abstract. We propose a superresolution method that exploits selfsimilarities and group structural information of image patches using only one single input frame. The superresolution problem is posed as learning the mapping between pairs of lowresolution and highresolution image patches. Instead of relying on an extrinsic set of training images as often required in examplebased superresolution algorithms, we employ a method that generates image pairs directly from the image pyramid of one single frame. The generated patch pairs are clustered for training a dictionary by enforcing group sparsity constraints underlying the image patches. Superresolution images are then constructed using the learned dictionary. Experimental results show the proposed method is able to achieve the stateoftheart performance. 1