Dynamic sparse support tracking with multiple measurement vectors using compressive MUSIC

Kim, Jong Min; Lee, Ok Kyun; Ye, Jong Chul

doi:10.1109/icassp.2012.6288478

Cited by 12 publications

(15 citation statements)

References 17 publications

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“…The papers on compressive sensing (CS) from 2005 [8], [9], [10], [11], [12], [13] (and many other more recent works) provide the missing theoretical guarantees -conditions for exact recovery and error bounds when exact recovery is not possible. In more recent works, the problem of recursively recovering a time sequence of sparse signals, with slowly changing sparsity patterns has also been studied [14], [15], [16], [17], [18], [19], [20], [21]. By "recursive" reconstruction, we mean that we want to use only the current measurements' vector and the previous reconstructed signal to recover the current signal.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…To the best of our knowledge, it has only been addressed in [15], and in very recent work [21]. The result of [21] is for exact dynamic support recovery in the noise-free case and it studies a different problem: the multiple measurement vector (MMV) version of the recursive recovery problem. The result from [15] for Least Squares CS-residual (LS-CS) stability) holds under mostly mild assumptions; its one limitation is that it assumes that support changes occur every p frames.…”

Section: Introductionmentioning

confidence: 99%

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Time Invariant Error Bounds for Modified-CS-Based Sparse Signal Sequence Recovery

Zhan

Vaswani

2015

IEEE Trans. Inform. Theory

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Abstract-In this work, we obtain performance guarantees for modified-CS and for its improved version, modified-CS-Add-LSDel, for recursive reconstruction of a time sequence of sparse signals from a reduced set of noisy measurements available at each time. Under mild assumptions, we show that the support recovery error of both algorithms is bounded by a time-invariant and small value at all times. The same is also true for the reconstruction error. Under a slow support change assumption, (i) the support recovery error bound is small compared to the support size; and (ii) our results hold under weaker assumptions on the number of measurements than what ℓ1 minimization for noisy data needs. We first give a general result that only assumes a bound on support size, number of support changes and number of small magnitude nonzero entries at each time. Later, we specialize the main idea of these results for two sets of signal change assumptions that model the class of problems in which a new element that is added to the support either gets added at a large initial magnitude or its magnitude slowly increases to a large enough value within a finite delay. Simulation experiments are shown to back up our claims.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Time Invariant Error Bounds for Modified-CS-Based Sparse Signal Sequence Recovery

Zhan

Vaswani

2015

IEEE Trans. Inform. Theory

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“…Recent work on Bayesian or other model-based approaches to recursive sparse estimation with time-varying supports includes [33], [34], [35], [36], [37]. The work of [13] gives an approximate batch solution for dynamic MRI that is quite fast, but is offline.…”

Section: B Related Workmentioning

confidence: 99%

“…The work of [46] obtains exact recovery thresholds for weighted 1 , similar to those in [48], for the case when a probabilistic prior on the signal support is available. Some later work motivated by modified-CS includes modified OMP [49], modified CoSaMP [50], modified block CS [51], error bounds on modified BPDN [52], [22], [53], [20], better conditions for modified-CS based exact recovery [54], and exact support recovery conditions for multiple measurement vectors (MMV) based recursive recovery [33].…”

Section: B Related Workmentioning

confidence: 99%

Recursive Reconstruction of Sparse Signal Sequences

Vaswani

2013

Compressed Sensing &Amp; Sparse Filtering

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In this chapter, we describe our recent work on the design and analysis of recursive algorithms for causally reconstructing a time sequence of (approximately) sparse signals from a greatly reduced number of linear projection measurements. The signals are sparse in some transform domain referred to as the sparsity basis and their sparsity patterns (support set of the sparsity basis coefficients) can change with time. By "recursive", we mean use only the previous signal's estimate and the current measurements to get the current signal's estimate. We also briefly summarize our exact reconstruction results for the noise-free case and our error bounds and error stability results (conditions under which a time-invariant and small bound on the reconstruction error holds at all times) for the noisy case. Connections with related work are also discussed.A key example application where the above problem occurs is dynamic magnetic resonance imaging (MRI) for real-time medical applications such as interventional radiology and MRI-guided surgery, or in functional MRI to track brain activation changes. Cross-sectional images of the brain, heart, larynx or other human organ images are piecewise smooth, and thus approximately sparse in the wavelet domain. In a time sequence, their sparsity pattern changes with time, but quite slowly. The same is also often true for the nonzero signal values. This simple fact, which was first observed in our work, is the key reason that our proposed recursive algorithms can achieve provably exact or accurate reconstruction from very few measurements.

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Jointly Optimized Target Detection and Tracking Using Compressive Samples

2019

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In this paper, we consider the problem of joint target detection and tracking in compressive sampling and processing (CSP-JDT). CSP can process the compressive samples of sparse signals directly without signal reconstruction, which is suitable for handling high-resolution radar signals. However, in CSP, the radar target detection and tracking problems are usually solved separately or by a two-stage strategy, which cannot obtain a globally optimal solution. To jointly optimize the target detection and tracking performance and inspired by the optimal Bayes joint decision and estimation (JDE) framework, a jointly optimized target detection and tracking algorithm in CSP is proposed. Since detection and tracking are highly correlated, we first develop a measurement matrix construction method to acquire the compressive samples, and then a joint CSP Bayesian approach is developed for target detection and tracking. The experimental results demonstrate that the proposed method outperforms the two-stage algorithms in terms of the joint performance metric. INDEX TERMSCompressive samples, joint decision and estimation, joint detection and tracking, joint performance metric.

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Dynamic sparse support tracking with multiple measurement vectors using compressive MUSIC

Cited by 12 publications

References 17 publications

Time Invariant Error Bounds for Modified-CS-Based Sparse Signal Sequence Recovery

Time Invariant Error Bounds for Modified-CS-Based Sparse Signal Sequence Recovery

Recursive Reconstruction of Sparse Signal Sequences

Jointly Optimized Target Detection and Tracking Using Compressive Samples

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