Unsupervised deconvolution of sparse spike trains using stochastic approximation

Champagnat, Frédéric; Goussard, Yves; Idier, Jérôme

doi:10.1109/78.553473

Cited by 78 publications

(76 citation statements)

References 29 publications

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“…Rather than specifying the prior probability density function (pdf) p(a) directly, we will specify p(a|b) and p(b), as previously done in [23], [25], [32]. To ensure consistency with Section II-A, p(a|b) must be chosen such that (3) is true and p(b) must be chosen such that b ∈ C is guaranteed.…”

Section: B Parameter Priorsmentioning

confidence: 99%

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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: B Parameter Priorsmentioning

confidence: 99%

“…For this, following [23], [25], [32], [37], it will be convenient to introduce the binary indicator sequence…”

Section: Introductionmentioning

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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show abstract

“…In this respect, the work of Knight and Fu [44] gives some interesting indications. Another approach may be to combine estimation and inference (by traditional stochastic samples) in a Bayesian framework that explicitly uses the prior distribution of the discrete time input signal [45][46][47].…”

Section: Discussionmentioning

confidence: 99%

Activelets: Wavelets for sparse representation of hemodynamic responses

et al. 2011

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a b s t r a c tWe propose a new framework to extract the activity-related component in the BOLD functional magnetic resonance imaging (fMRI) signal. As opposed to traditional fMRI signal analysis techniques, we do not impose any prior knowledge of the event timing. Instead, our basic assumption is that the activation pattern is a sequence of short and sparsely distributed stimuli, as is the case in slow event-related fMRI.We introduce new wavelet bases, termed ''activelets'', which sparsify the activityrelated BOLD signal. These wavelets mimic the behavior of the differential operator underlying the hemodynamic system. To recover the sparse representation, we deploy a sparse-solution search algorithm.The feasibility of the method is evaluated using both synthetic and experimental fMRI data. The importance of the activelet basis and the non-linear sparse recovery algorithm is demonstrated by comparison against classical B-spline wavelets and linear regularization, respectively.

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“…Many approximations to this optimization have been proposed which result to different algorithms for this detection-estimation problem [14]. Many Monte Carlo techniques have also been proposed for generating samples of z and x from the posterior and thus compute the PM estimates of x.…”

Section: Appropriate Modeling Of Input Signalmentioning

confidence: 99%

Bayesian inference for inverse problems

Mohammad‐Djafari

2002

AIP Conference Proceedings

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Abstract. Traditionally, the MaxEnt workshops start by a tutorial day. This paper summarizes my talk during 2001'th workshop at John Hopkins University. The main idea in this talk is to show how the Bayesian inference can naturally give us all the necessary tools we need to solve real inverse problems: starting by simple inversion where we assume to know exactly the forward model and all the input model parameters up to more realistic advanced problems of myopic or blind inversion where we may be uncertain about the forward model and we may have noisy data.Starting by an introduction to inverse problems through a few examples and explaining their ill posedness nature, I briefly presented the main classical deterministic methods such as data matching and classical regularization methods to show their limitations. I then presented the main classical probabilistic methods based on likelihood, information theory and maximum entropy and the Bayesian inference framework for such problems. I show that the Bayesian framework, not only generalizes all these methods, but also gives us natural tools, for example, for inferring the uncertainty of the computed solutions, for the estimation of the hyperparameters or for handling myopic or blind inversion problems. Finally, through a deconvolution problem example, I presented a few state of the art methods based on Bayesian inference particularly designed for some of the mass spectrometry data processing problems.

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Unsupervised deconvolution of sparse spike trains using stochastic approximation

Cited by 78 publications

References 29 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

Activelets: Wavelets for sparse representation of hemodynamic responses

Bayesian inference for inverse problems

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