Blind deconvolution via cumulant extrema
TL;DR: This article provides a tutorial description as well as presenting new results on many of the fundamental higher-order concepts used in deconvolution, with the emphasis on maximizing the deconvolved signal's normalized cumulant.
Abstract: Classical deconvolution is concerned with the task of recovering an excitation signal, given the response of a known time-invariant linear operator to that excitation Deconvolution is discussed along with its more challenging counterpart, blind deconvolution, where no knowledge of the linear operator is assumed This discussion focuses on a class of deconvolution algorithms based on higher-order statistics, and more particularly, cumulants These algorithms offer the potential of superior performance in both the noise free and noisy data cases relative to that achieved by other deconvolution techniques This article provides a tutorial description as well as presenting new results on many of the fundamental higher-order concepts used in deconvolution, with the emphasis on maximizing the deconvolved signal's normalized cumulant
Citations
More filters
01 Aug 1997
TL;DR: A number of recently developed concepts and techniques for BSI, which include the concept of blind system identifiability in a deterministic framework, the blind techniques of maximum likelihood and subspace for estimating the system's impulse response, and other techniques for direct estimation of the system input are reviewed.
Abstract: Blind system identification (BSI) is a fundamental signal processing technology aimed at retrieving a system's unknown information from its output only. This technology has a wide range of possible applications such as mobile communications, speech reverberation cancellation, and blind image restoration. This paper reviews a number of recently developed concepts and techniques for BSI, which include the concept of blind system identifiability in a deterministic framework, the blind techniques of maximum likelihood and subspace for estimating the system's impulse response, and other techniques for direct estimation of the system input.
358 citations
TL;DR: In this paper, the authors proposed the use of the minimum entropy deconvolution (MED) technique to enhance the ability of the existing autoregressive (AR) model based filtering technique to detect localised faults in gears.
351 citations
TL;DR: The present study introduces a different approach to parameterizing the inverse filter, and proposes to model the inverse transfer function as a member of a principal shift-invariant subspace, which results in considerably more stable reconstructions as compared to standard parameterization methods.
Abstract: The problem of reconstruction of ultrasound images by means of blind deconvolution has long been recognized as one of the central problems in medical ultrasound imaging. In this paper, this problem is addressed via proposing a blind deconvolution method which is innovative in several ways. In particular, the method is based on parametric inverse filtering, whose parameters are optimized using two-stage processing. At the first stage, some partial information on the point spread function is recovered. Subsequently, this information is used to explicitly constrain the spectral shape of the inverse filter. From this perspective, the proposed methodology can be viewed as a ldquohybridizationrdquo of two standard strategies in blind deconvolution, which are based on either concurrent or successive estimation of the point spread function and the image of interest. Moreover, evidence is provided that the ldquohybridrdquo approach can outperform the standard ones in a number of important practical cases. Additionally, the present study introduces a different approach to parameterizing the inverse filter. Specifically, we propose to model the inverse transfer function as a member of a principal shift-invariant subspace. It is shown that such a parameterization results in considerably more stable reconstructions as compared to standard parameterization methods. Finally, it is shown how the inverse filters designed in this way can be used to deconvolve the images in a nonblind manner so as to further improve their quality. The usefulness and practicability of all the introduced innovations are proven in a series of both in silico and in vivo experiments. Finally, it is shown that the proposed deconvolution algorithms are capable of improving the resolution of ultrasound images by factors of 2.24 or 6.52 (as judged by the autocorrelation criterion) depending on the type of regularization method used.
151 citations
Cites background or methods from "Blind deconvolution via cumulant ex..."
...The deconvolution method described here is based on the concept of inverse filtering as in [12] and [24]....
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...the PSF and the reflectivity function concurrently [23], [24]....
[...]
...Certainly, the most common parametrization of is by the samples of its corresponding impulse response [12], [24]....
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102 citations
TL;DR: Higher order statistical method called independent component analysis (ICA) is introduced as a novel tool for analysis of gas-sensor array measurement data and is shown to be capable of handling sensor drift combined with improved discrimination, dimensionality reduction, and more adequate data representation when compared to PCA.
Abstract: The performance of gas-sensor array systems is greatly influenced by the pattern recognition scheme applied on the instrument's measurement data. The traditional method of choice is principal component analysis (PCA), aiming for reduction in dimensionality and visualization of multivariate measurement data. PCA, as a second-order statistical tool, performs well in many cases, but lacks the ability to give meaningful representations for non-Gaussian data, which often is a property of gas-sensor array measurement data. If, instead, higher order statistical methods are considered for data analysis, more useful information can be extracted from the data. This paper introduces the higher order statistical method called independent component analysis (ICA) as a novel tool for analysis of gas-sensor array measurement data. A comparison between the performances of PCA and ICA is illustrated both in theory and for two sets of practical measurement data. The described experiments show that ICA is capable of handling sensor drift combined with improved discrimination, dimensionality reduction, and more adequate data representation when compared to PCA.
93 citations
Cites methods from "Blind deconvolution via cumulant ex..."
...Secondorder methods use the variance within the data to estimate the transform, while higher order methods exploit the information about the data density that is not contained in the covariance structure, that is, cumulants and moments of order greater than two2 [ 8 ]....
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References
More filters
IBM1
TL;DR: This paper solves the general problem of adaptive channel equalization without resorting to a known training sequence or to conditions of limited distortion.
Abstract: Conventional equalization and carrier recovery algorithms for minimizing mean-square error in digital communication systems generally require an initial training period during which a known data sequence is transmitted and properly synchronized at the receiver. This paper solves the general problem of adaptive channel equalization without resorting to a known training sequence or to conditions of limited distortion. The criterion for equalizer adaptation is the minimization of a new class of nonconvex cost functions which are shown to characterize intersymbol interference independently of carrier phase and of the data symbol constellation used in the transmission system. Equalizer convergence does not require carrier recovery, so that carrier phase tracking can be carried out at the equalizer output in a decision-directed mode. The convergence properties of the self-recovering algorithms are analyzed mathematically and confirmed by computer simulation.
2,645 citations
01 Mar 1991
TL;DR: A compendium of recent theoretical results associated with using higher-order statistics in signal processing and system theory is provided, and the utility of applying higher- order statistics to practical problems is demonstrated.
Abstract: A compendium of recent theoretical results associated with using higher-order statistics in signal processing and system theory is provided, and the utility of applying higher-order statistics to practical problems is demonstrated. Most of the results are given for one-dimensional processes, but some extensions to vector processes and multichannel systems are discussed. The topics covered include cumulant-polyspectra formulas; impulse response formulas; autoregressive (AR) coefficients; relationships between second-order and higher-order statistics for linear systems; double C(q,k) formulas for extracting autoregressive moving average (ARMA) coefficients; bicepstral formulas; multichannel formulas; harmonic processes; estimates of cumulants; and applications to identification of various systems, including the identification of systems from just output measurements, identification of AR systems, identification of moving-average systems, and identification of ARMA systems. >
1,854 citations
TL;DR: The strengths and limitations of correlation-based signal processing methods, with emphasis on the bispectrum and trispectrum, and the applications of higher-order spectra in signal processing are discussed.
Abstract: The strengths and limitations of correlation-based signal processing methods are discussed. The definitions, properties, and computation of higher-order statistics and spectra, with emphasis on the bispectrum and trispectrum are presented. Parametric and nonparametric expressions for polyspectra of linear and nonlinear processes are described. The applications of higher-order spectra in signal processing are discussed. >
931 citations
NEC1
TL;DR: A self-recovering equalization algorithm, which is employed in multilevel amplitude-modulated data transmission, is presented and the convergence processes of the present self-reaching equalizer are shown by computer simulation.
Abstract: A self-recovering equalization algorithm, which is employed in multilevel amplitude-modulated data transmission, is presented. Such a self-recovering equalizer has been required when time-division multiplexed (TDM) voice or picturephone PCM signals must be transmitted over the existing frequency-division multiplexed (FDM) transmission channel. The present self-recovering equalizer is quite simple, as is a conventional binary equalizer. The convergence processes of the present self-recovering equalizer are shown by computer simulation. Some theoretical considerations on this convergence process are also added.
909 citations
TL;DR: A necessary and sufficient condition for blind deconvolution (without observing the input) of nonminimum-phase linear time-invariant systems (channels) is derived and several optimization criteria are proposed, and their solution is shown to correspond to the desired response.
Abstract: A necessary and sufficient condition for blind deconvolution (without observing the input) of nonminimum-phase linear time-invariant systems (channels) is derived. Based on this condition, several optimization criteria are proposed, and their solution is shown to correspond to the desired response. These criteria involve the computation only of second- and fourth-order moments, implying a simple tap update procedure. The proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the (unobserved) input sequence. It is shown that in several important cases (e.g. when the additive noise is Gaussian), the proposed criteria are essentially unaffected. >
843 citations