Methods for Sparse Signal Recovery Using Kalman Filtering With Embedded Pseudo-Measurement Norms and Quasi-Norms

Carmi, Avishy; Gurfil, Pini; Kanevsky, Dimitri

doi:10.1109/tsp.2009.2038959

Cited by 139 publications

(156 citation statements)

References 10 publications

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“…Kalman filters [2][3][4][5] are used in a variety of applications ranging from economics to vehicle navigation, especially for tracking the value of dynamic parameters in noisy environments. They can also be used for the reconstruction of a signal with fewer samples in real time by applying a two step recursive process: (a) prediction, where the current state variables are estimated, and (b) update of the estimated values, when the next measurement is available.…”

Section: Open Accessmentioning

confidence: 99%

Undersampling in Orthogonal Frequency Division Multiplexing Telecommunication Systems

Petrellis¹

2014

Applied Sciences

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Several techniques have been proposed that attempt to reconstruct a sparse signal from fewer samples than the ones required by the Nyquist theorem. In this paper, an undersampling technique is presented that allows the reconstruction of the sparse information that is transmitted through Orthogonal Frequency Division Multiplexing (OFDM) modulation. The properties of the Discrete Fourier Transform (DFT) that is employed by the OFDM modulation, allow the estimation of several samples from others that have already been obtained on the side of the receiver, provided that special relations are valid between the original data values. The inherent sparseness of the original data, as well as the Forward Error Correction (FEC) techniques employed, can assist the information recovery from fewer samples. It will be shown that up to 1/4 of the samples can be omitted from the sampling process and substituted by others on the side of the receiver for the successful reconstruction of the original data. In this way, the size of the buffer memory used for sample storage, as well as the storage requirements of the Fast Fourier Transform (FFT) implementation at the receiver, may be reduced by up to 25%. The power consumption of the Analog Digital Converter on the side of the receiver is also reduced when a lower sampling rate is used.

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Section: Open Accessmentioning

confidence: 99%

Undersampling in Orthogonal Frequency Division Multiplexing Telecommunication Systems

Petrellis¹

2014

Applied Sciences

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“…Secondly, the employment of hyper-parameters to model state innovation promotes sparsity. Thirdly, different from previous work in [6,7,8,9], the proposed model only involves one parameter σ 2 that needs to be manually adjusted. In principle, this parameter can also be learned from the measurements y t [1].…”

Section: Hierarchical Bayesian Kalman Filtermentioning

confidence: 98%

“…The essential idea behind [6] and [7] is to apply thresholds that enforce sparsity. Work in [8] adopts a probabilistic model but signal amplitudes and support are estimated separately.…”

Section: The Kalman Filter and The Related Approachesmentioning

confidence: 99%

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Tracking dynamic sparse signals using Hierarchical Bayesian Kalman filters

Karseras

Leung

Dai

2013

2013 IEEE International Conference on Acoustics, Speech and Signal Processing

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In this work we are interested in the problem of reconstructing time-varying signals for which the support is assumed to be sparse. For a single time instance it is possible to reconstruct the original signal efficiently by employing a suitable algorithm for sparse signal recovery, given the sparsity level of the signal. In the case of time-varying sparse signals the sparsity level is not necessarily known a-priori. Furthermore conventional tracking by Kalman filtering fails to promote sparsity. Instead, a hierarchical Bayesian model is used in the tracking process which succeeds in modelling sparsity. One theorem is provided that extends previous work by providing some more general results. A second theorem gives the conditions under which all sparse signals are recovered exactly. It is demonstrated that the proposed method succeeds in recovering timevarying sparse signals with greater accuracy than the classic Kalman filter approach.

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“…A modification of KF-CS was introduced in [32]. Recent work on Bayesian or other model-based approaches to recursive sparse estimation with time-varying supports includes [33], [34], [35], [36], [37].…”

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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Methods for Sparse Signal Recovery Using Kalman Filtering With Embedded Pseudo-Measurement Norms and Quasi-Norms

Cited by 139 publications

References 10 publications

Undersampling in Orthogonal Frequency Division Multiplexing Telecommunication Systems

Undersampling in Orthogonal Frequency Division Multiplexing Telecommunication Systems

Tracking dynamic sparse signals using Hierarchical Bayesian Kalman filters

Recursive Reconstruction of Sparse Signal Sequences

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