Deconvolution of sparse spike trains by iterated window maximization

Kaaresen, Kjetil F.

doi:10.1109/78.575692

Cited by 62 publications

(40 citation statements)

References 21 publications

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“…Usually, alternating minimization algorithms are used to estimate signal x and impulse response h by minimizing the cost function, which often comprises a data fidelity term and a regularization term (penalty term). The regularization term is adopted to exploit the prior information, such as the sparsity of the sources [36,37,40], as considered in [36] for seismic signals, in [10] [21] for spike signals, and in [22] for images. In blind source separation, however, apart from the sparsity that is often assumed for the underdetermined case [28] [43], statistical independence between the sources is also widely exploited for estimating the sources and the mixing channels [9,18,19,29,30,34,39].…”

Section: Introductionmentioning

confidence: 99%

Sparse Blind Speech Deconvolution with Dynamic Range Regularization and Indicator Function

Guan

Wang

2017

Circuits Syst Signal Process

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Blind deconvolution is an ill-posed problem. To solve such a problem, prior information, such as, the sparseness of the source (i.e. input) signal or channel impulse responses, is usually adopted. In speech deconvolution, the source signal is not naturally sparse. However, the direct impulse and early reflections of the impulse responses of an acoustic system can be considered as sparse. In this paper, we exploit the channel sparsity and present an algorithm for speech deconvolution, where the dynamic range of the convolutive speech is also used as the prior information. In this algorithm, the estimation of the impulse response and the source signal is achieved by alternating between two steps, namely, the ℓ 1 regularized least squares optimization and a proximal operation. As demonstrated in our experiments, the proposed method provides superior performance for deconvolution of a sparse acoustic system, as compared with two state-of-the-art methods.

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Section: Introductionmentioning

confidence: 99%

Sparse Blind Speech Deconvolution with Dynamic Range Regularization and Indicator Function

Guan

Wang

2017

Circuits Syst Signal Process

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“…Early techniques implicitly assumed known, constant, Gaussian white noise-from Wiener filters, which often overblurred locally sharp features, to autocorrelation-based techniques and CLEAN algorithms (Kaaresen 1997), which worked for point sources. More robust maximum-likelihood, maximum-entropy, and general probabilistic-based techniques such as Richardson-Lucy (Richardson 1972;Lucy 1974) and the EM algorithm (Dempster et al 1977) still often assumed a single uniform scale (usually the pixel size) for features in the ''true'' image.…”

Section: Introductionmentioning

confidence: 99%

An Image Restoration Technique with Error Estimates

Esch¹,

Connors²,

Karovska³

et al. 2004

ApJ

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Image restoration including deconvolution techniques offers a powerful tool to improve resolution in images and to extract information on the multiscale structure stored in astronomical observations. We present a new method for statistical deconvolution, which we call expectation through Markov Chain Monte Carlo (EMC2). This method is designed to remedy several shortfalls of currently used deconvolution and restoration techniques for Poisson data. We use a wavelet-like multiscale representation of the true image to achieve smoothing at all scales of resolution simultaneously, thus capturing detailed features in the image at the same time as larger scale extended features. Thus, this method smooths the image, while maintaining the ability to effectively reconstruct point sources and sharp features in the image. We use a principled, fully Bayesian model-based analysis, which produces extensive information about the uncertainty in the fitted smooth image, allowing assessment of the errors in the resulting reconstruction. Our method also includes automatic fitting of the multiscale smoothing parameters. We show several examples of application of EMC2 to both simulated data and a real astronomical X-ray source.

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“…The 1 norm penalty (i.e., φ n (x) = |x|) has been proposed for sparse deconvolution [10], [16], [41], [66] and more generally for sparse signal processing [15] and statistics [67]. For the 1 norm and other non-differentiable convex penalties, efficient algorithms for large scale problems of the form (1) and similar (including convex constraints) have been developed based on proximal splitting methods [18], [19], alternating direction method of multipliers (ADMM) [9], majorization-minimization (MM) [25], primal-dual gradient descent [22], and Bregman iterations [36].…”

Section: B Related Work (Sparsity Penalized Least Squares)mentioning

confidence: 99%

Sparse Signal Estimation by Maximally Sparse Convex Optimization

Selesnick¹,

Bayram

2014

IEEE Trans. Signal Process.

162

125

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Abstract-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 nonconvex 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.

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Deconvolution of sparse spike trains by iterated window maximization

Abstract: This research report is organized as two separate papers. The first paper describes a new deconvolution algorithm for sparse spike trains. The second paper compares the new algorithm to a number of existing alternatives.

Cited by 62 publications

References 21 publications

Sparse Blind Speech Deconvolution with Dynamic Range Regularization and Indicator Function

Sparse Blind Speech Deconvolution with Dynamic Range Regularization and Indicator Function

An Image Restoration Technique with Error Estimates

Sparse Signal Estimation by Maximally Sparse Convex Optimization

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