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36
Trust, but verify: Fast and accurate signal recovery from 1-bit compressive measurements
, 2010
"... Abstract—The recently emerged compressive sensing (CS) framework aims to acquire signals at reduced sample rates compared to the classical Shannon-Nyquist rate. To date, the CS theory has assumed primarily real-valued measurements; it has recently been demonstrated that accurate and stable signal ac ..."
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Cited by 29 (2 self)
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Abstract—The recently emerged compressive sensing (CS) framework aims to acquire signals at reduced sample rates compared to the classical Shannon-Nyquist rate. To date, the CS theory has assumed primarily real-valued measurements; it has recently been demonstrated that accurate and stable signal acquisition is still possible even when each measurement is quantized to just a single bit. This property enables the design of simplified CS acquisition hardware based around a simple sign comparator rather than a more complex analog-to-digital converter; moreover, it ensures robustness to gross non-linearities applied to the measurements. In this paper we introduce a new algorithm — restricted-step shrinkage (RSS) — to recover sparse signals from 1-bit CS measurements. In contrast to previous algorithms for 1-bit CS, RSS has provable convergence guarantees, is about an order of magnitude faster, and achieves higher average recovery signal-to-noise ratio. RSS is similar in spirit to trust-region methods for non-convex optimization on the unit sphere, which are relatively unexplored in signal processing and hence of independent interest. Index Terms—1-bit compressive sensing, quantization, consistent reconstruction, trust-region algorithms I.
Recursive sparse recovery in large but correlated noise
- in Proc. 49th Allerton Conf. Commun. Control Comput
, 2011
"... Abstract—In this work, we focus on the problem of recursively recovering a time sequence of sparse signals, with time-varying sparsity patterns, from highly undersampled measurements cor-rupted by very large but correlated noise. It is assumed that the noise is correlated enough to have an approxima ..."
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Cited by 20 (13 self)
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Abstract—In this work, we focus on the problem of recursively recovering a time sequence of sparse signals, with time-varying sparsity patterns, from highly undersampled measurements cor-rupted by very large but correlated noise. It is assumed that the noise is correlated enough to have an approximately low rank covariance matrix that is either constant, or changes slowly, with time. We show how our recently introduced Recursive Projected CS (ReProCS) and modified-ReProCS ideas can be used to solve this problem very effectively. To the best of our knowledge, except for the recent work of dense error correction via ℓ1 minimization, which can handle another kind of large but “structured ” noise (the noise needs to be sparse), none of the other works in sparse recovery have studied the case of any other kind of large noise. I.
Reprocs: A missing link between recursive robust pca and recursive sparse recovery in large but correlated noise
- CoRR
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Sparse Signal Estimation by Maximally Sparse Convex Optimization
- IEEE TRANSACTIONS ON SIGNAL PROCESSING
, 2014
"... This paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing, e.g. sparse deconvolution. This paper aims to induce sparsity more strongly than L1 norm regularization, while avoiding non-convex optimization. For this purpose, this paper describes ..."
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Cited by 8 (4 self)
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This paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing, e.g. sparse deconvolution. This paper aims to induce sparsity more strongly than L1 norm regularization, while avoiding non-convex optimization. For this purpose, this paper describes the design and use of non-convex penalty functions (regularizers) constrained so as to ensure the convexity of the total cost function, F, to be minimized. The method is based on parametric penalty functions, the parameters of which are constrained to ensure convexity of F. It is shown that optimal parameters can be obtained by semidefinite programming (SDP). This maximally sparse convex (MSC) approach yields maximally non-convex sparsity-inducing penalty functions constrained such that the total cost function, F, is convex. It is demonstrated that iterative MSC (IMSC) can yield solutions substantially more sparse than the standard convex sparsity-inducing approach, i.e., L1 norm minimization.
1 Compressive Sensing Based High Resolution Channel Estimation for OFDM System
"... Abstract — Orthogonal frequency division multiplexing (OFDM) is a technique that will prevail in the next generation wireless communication. Channel estimation is one of the key challenges in OFDM, since high-resolution channel estimation can significantly improve the equalization at the receiver an ..."
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Cited by 7 (3 self)
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Abstract — Orthogonal frequency division multiplexing (OFDM) is a technique that will prevail in the next generation wireless communication. Channel estimation is one of the key challenges in OFDM, since high-resolution channel estimation can significantly improve the equalization at the receiver and consequently enhance the communication performances. In this paper, we propose a system with an asymmetric DAC/ADC pair and formulate OFDM channel estimation as a compressive sensing problem. By skillfully designing pilots and taking advantages of the sparsity of the channel impulse response, the proposed system realizes high resolution channel estimation at a low cost. The pilot design, the use of a high-speed DAC and a regular-speed ADC, and the estimation algorithm tailored for channel estimation distinguish the proposed approach from the existing estimation approaches. We theoretically show that in the proposed system, a N-resolution channel can be faithfully obtained with an ADC speed at M = O(S 2 log(N/S)), where N is also the DAC speed and S is the channel impulse response sparsity. Since S is small and increasing the DAC speed to N> M is relatively cheap, we obtain a high-resolution channel at a low cost. We also present a novel estimator that is both faster and more accurate than the typical ℓ1 minimization. In the numerical experiments, we simulated various numbers of multipaths and different SNRs and let the transmitter DAC run at 16 times the speed of the receiver ADC for estimating channels at the 16x resolution. While there is no similar approaches (for asymmetric DAC/ADC pairs) to compare with, we derive the Cramér-Rao lower bound. I.
An adaptive inverse scale space method for compressed sensing
, 2011
"... In this paper we introduce a novel adaptive approach for solving ℓ 1-minimization problems as frequently arising in compressed sensing, which is based on the recently introduced inverse scale space method. The scheme allows to efficiently compute minimizers by solving a sequence of low-dimensional n ..."
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Cited by 6 (2 self)
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In this paper we introduce a novel adaptive approach for solving ℓ 1-minimization problems as frequently arising in compressed sensing, which is based on the recently introduced inverse scale space method. The scheme allows to efficiently compute minimizers by solving a sequence of low-dimensional nonnegative least-squares problems. We provide a detailed convergence analysis in a general setup as well as refined results under special conditions. In addition we discuss experimental observations in several numerical examples.
Exact Reconstruction Conditions for Regularized Modified Basis Pursuit
, 2010
"... is a continuous and unimodal function of 2, with the unique maximum 2 2 (p+1) 2 (p) achieved at = ( ) , see also (9a). We conclude that ( ) 0 ( 2) (p+1) must go to zero. The second claim of Theorem 1 follows. ..."
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Cited by 4 (2 self)
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is a continuous and unimodal function of 2, with the unique maximum 2 2 (p+1) 2 (p) achieved at = ( ) , see also (9a). We conclude that ( ) 0 ( 2) (p+1) must go to zero. The second claim of Theorem 1 follows.
Accessed
, 2012
"... Background. Accumulating evidence supports leukocyte telomere length (LTL) as a biological marker of cellular aging. Poor sleep is a risk factor for age-related disease; however, the extent to which sleep accounts for variation in LTL is unknown. Methods. The present study examined associations of ..."
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Cited by 3 (0 self)
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Background. Accumulating evidence supports leukocyte telomere length (LTL) as a biological marker of cellular aging. Poor sleep is a risk factor for age-related disease; however, the extent to which sleep accounts for variation in LTL is unknown. Methods. The present study examined associations of self-reported sleep duration, onset latency, and subjective quality with LTL in a communitydwelling sample of 245 healthy women in midlife (aged 49-66 years). Results. While sleep duration and onset latency were unrelated to LTL, women reporting poorer sleep quality displayed shorter LTL (r = 0.14, P = 0.03), independent of age, BMI, race, and income (b = 55.48, SE = 27.43, P = 0.04). When analyses were restricted to participants for whom sleep patterns were chronic, poorer sleep quality predicted shorter LTL independent of covariates and perceived psychological stress. Conclusions. This study provides the first evidence that poor sleep quality explains significant variation in LTL, a marker of cellular aging.
High resolution OFDM channel estimation with low speed ADC using compressive sensing
- in proceedings of IEEE International Conference on Communications
, 2011
"... Abstract — Orthogonal frequency division multiplexing (OFDM) is a technique that will prevail in the next generation wireless communication. Channel estimation is one of the key challenges in an OFDM system. In this paper, we formulate OFDM channel estimation as a compressive sensing problem, which ..."
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Cited by 2 (2 self)
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Abstract — Orthogonal frequency division multiplexing (OFDM) is a technique that will prevail in the next generation wireless communication. Channel estimation is one of the key challenges in an OFDM system. In this paper, we formulate OFDM channel estimation as a compressive sensing problem, which takes advantage of the sparsity of the channel impulse response and reduces the number of probing measurements, which in turn reduces the ADC speed needed for channel estimation. Specifically, we propose sending out pilots with random phases in order to “spread out ” the sparse taps in the impulse response over the uniformly downsampled measurements at the low speed receiver ADC, so that the impulse response can still be recovered by sparse optimization. This contribution leads to high resolution channel estimation with low speed ADCs, distinguishing this paper from the existing attempts of OFDM channel estimation. We also propose a novel estimator that performs better than the commonly used ℓ1 minimization. Specifically, it significantly reduces estimation error by combing ℓ1 minimization with iterative support detection and limited-support least-squares. While letting the receiver ADC run at a speed as low as 1/16 of the speed of the transmitter DAC, we simulated various numbers of multipaths and different measurement SNRs. The proposed system has channel estimation resolution as high as the system equipped with the high speed ADCs, and the proposed algorithm provides additional 6 dB gain for signal to noise ratio. I.
