A partially collapsed Gibbs sampler for parameters with local constraints

Kail, Georg; Tourneret, Jean-Yves; Hlawatsch, Franz; Dobigeon, Nicolas

doi:10.1109/icassp.2010.5495806

Cited by 7 publications

(11 citation statements)

References 9 publications

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“…This makes it potentially interesting for many signal processing applications including signal segmentation [49], optical coherence tomography [50], electromyography [10], [11], and electrocardiography [13], [51]. Furthermore, the minimum distance constraint itself can be generalized to a wider class of "local deterministic constraints," which can be exploited in an analogous way [36].…”

Section: Discussionmentioning

confidence: 99%

Blind Deconvolution of Sparse Pulse Sequences Under a Minimum Distance Constraint: A Partially Collapsed Gibbs Sampler Method

Kail¹,

Tourneret

Hlawatsch³

et al. 2012

IEEE Trans. Signal Process.

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Abstract-For blind deconvolution of an unknown sparse sequence convolved with an unknown pulse, a powerful Bayesian method employs the Gibbs sampler in combination with a Bernoulli-Gaussian prior modeling sparsity. In this paper, we extend this method by introducing a minimum distance constraint for the pulses in the sequence. This is physically relevant in applications including layer detection, medical imaging, seismology, and multipath parameter estimation. We propose a Bayesian method for blind deconvolution that is based on a modified Bernoulli-Gaussian prior including a minimum distance constraint factor. The core of our method is a partially collapsed Gibbs sampler (PCGS) that tolerates and even exploits the strong local dependencies introduced by the minimum distance constraint. Simulation results demonstrate significant performance gains compared to a recently proposed PCGS. The main advantages of the minimum distance constraint are a substantial reduction of computational complexity and of the number of spurious components in the deconvolution result.

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Section: Discussionmentioning

confidence: 99%

Blind Deconvolution of Sparse Pulse Sequences Under a Minimum Distance Constraint: A Partially Collapsed Gibbs Sampler Method

Kail¹,

Tourneret

Hlawatsch³

et al. 2012

IEEE Trans. Signal Process.

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“…As pointed out in [27], this classical GS is poorly suited to problems with local constraints because a constraint that excludes parts of the hypothesis space may even inhibit convergence to p (b, a, h, σ 2 n |x) altogether.…”

Section: Algorithm 1 the Classical Gsmentioning

confidence: 99%

“…In order to handle both positive and negative wave amplitudes, a k is distributed according to a zero mean Gaussian distribution with variance σ where d depends on the RR interval length. Consequently, the T-wave detection problem can be seen as a BG blind deconvolution problem with deterministic local constraints as in [26], [27]. The prior of b can then be defined as the product of a minimum-distance constraint indicator function I C (b) and the likelihood of independent Bernoulli random variables…”

Section: B Prior Distributionsmentioning

confidence: 99%

“…This report concentrates on a particular MCMC method referred to as partially collapsed Gibbs sampler (PCGS) whose convergence properties have been studied in [24]. The PCGS has shown interesting properties for electromyography (EMG) [25] and optical coherence tomography (OCT) [26], [27]. However, to our knowledge, it is the first time a PCGS is applied for P and T-wave delineation in ECG signals.…”

Section: Introductionmentioning

confidence: 99%

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P- and T-Wave Delineation in ECG Signals Using a Bayesian Approach and a Partially Collapsed Gibbs Sampler

Lin

Mailhes

Tourneret

2010

IEEE Trans. Biomed. Eng.

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104

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Detection and delineation of P and T-waves are important parts in the analysis and interpretation of ECG signals. This report approaches this problem using Bayesian inference to represent a priori relationships among ECG wave components. Based on the recently introduced partially collapsed Gibbs sampler principle, the wave delineation and estimation are conducted simultaneously by using a Bayesian algorithm combined with a Markov chain Monte Carlo method. This method exploits the strong local dependency of ECG signals. The proposed strategy is evaluated on the annotated QT database and compared to other classical algorithms. An important property of this work is that it allows not only the detection of wave peaks and boundaries, but also the estimation of P and T waveforms for each analysis window. This can be useful for some ECG analysis that require wave morphology information. Index TermsECG, P and T-wave delineation, hierarchical Bayesian analysis, partially collapsed Gibbs sampling, Markov chain Monte Carlo method.

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“…Here, we propose a partially collapsed Gibbs sampler (PCGS) [8,9] for joint estimation of the MPC parameters (number, timesof-arrival, angles-of-arrival, and amplitudes) and of the pulse shape. The PCGS is a Markov chain Monte Carlo method [10] that is well suited for joint estimation of a large number of possibly strongly dependent parameters.…”

Section: Introductionmentioning

confidence: 99%

Direction-resolved estimation of multipath parameters for UWB channels: A partially collapsed Gibbs sampler method

Kail

Witrisal

Hlawatsch

2011

2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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We propose a Monte Carlo method for determining the parameters of multipath components (MPCs) for ultra-wideband channels. A partially collapsed Gibbs sampler is used for jointly estimating the number, times-of-arrival, angles-of-arrival, and amplitudes of the MPCs as well as the sounding pulse from signals received by a 2D antenna array. Our system model accounts for propagation delays between the receive antennas. Temporal-angular sparsity of the detected MPCs is ensured by a 2D minimum distance constraint. Numerical results for synthetic and real signals demonstrate the excellent performance and fast convergence of our method.

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A partially collapsed Gibbs sampler for parameters with local constraints

Cited by 7 publications

References 9 publications

Blind Deconvolution of Sparse Pulse Sequences Under a Minimum Distance Constraint: A Partially Collapsed Gibbs Sampler Method

Blind Deconvolution of Sparse Pulse Sequences Under a Minimum Distance Constraint: A Partially Collapsed Gibbs Sampler Method

P- and T-Wave Delineation in ECG Signals Using a Bayesian Approach and a Partially Collapsed Gibbs Sampler

Direction-resolved estimation of multipath parameters for UWB channels: A partially collapsed Gibbs sampler method

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