Abstract: It is pointed out that certain criteria proposed in the paper by Shalvi and Weinstein (see ibid., vol.36, no.2, p.312-21, 1990) have been proposed before in the context of real-valued signals. Furthermore, it is noted that the assertion made in the paper that all local maxima of the proposed criteria correspond to the desired equalizer solution, holds true, strictly speaking, only for infinite length equalizers. There exist counterexamples which show existence of false local maxima when finite-length equalizers are used. Finally, it is also noted that in the presence of additive Gaussian noise of unknown power spectral density at the input to the equalizer (equivalently, at the channel output), it is not clear if the methods proposed in the paper will yield the desired response up to a constant gain. >

Abstract: A technique for deconvolving an image from both a single convolution and an ensemble of differently blurred images is presented. The method is more robust than the earlier blind deconvolution algorithms proposed by Ayers and Dainty [ Opt. Lett.13, 547 ( 1988)] and Davey et al. [ Opt. Commun.69, 353 ( 1989)]. The performance of the algorithm in the presence of noise is evaluated. It is also demonstrated how the algorithm can be modified to utilize the much greater amount of information contained in an ensemble of differently blurred pictures of an image. Reconstructions using both computer simulations and infrared astronomical speckle data are presented. The speckle reconstructions are compared with those obtained by both Fourier phase retrieval and bispectral estimation.

Abstract: Preface. 1. Convolution. Introduction. Convolution in geophysics. Fourier theory. Geophysical convolution model. 2. Deconvolution. Introduction. Predictive deconvolution. Time-varying deconvolution. Homomorphic deconvolution. Minimum entropy deconvolution. 3. Inverse Theory. Introduction. Linearized inversion. Nonlinear inversion. Types of norms. 4. Inversion and Deconvolution. Introduction. Deconvolution and inversion. Multichannel constrained Wiener filter. Discussion. 5. Inversion of Reflection Seismic Data. Introduction. Seismic reflection method. Inversion methods. Migration. Seismic tomography. Ocean acoustic tomography. Stochastic tomography. 6. Inversion of Other Geophysical Data. Introduction. Inversion of gravity data. Inversion of magnetic data. Inversion of resistivity data. Inversion of electromagnetic data. Joint and cooperative inversion. 7. Deconvolution of Other Geophysical Data. Introduction. Estimation of density. Optimum filter for potential field data. Modified Wiener-Hopf equation. Nonstationarity of magnetic data. Kalman approach. Deconvolution of resistivity data. Deconvolution of paleomagnetic data. 8. Spectral Estimation. Introduction. Overview of conventional methods. High resolution methods. Multichannel and multidimensional spectra. Appendix A. Multichannel Unimodular Constrained Filter. References. Subject Index.

Abstract: A method and apparatus for controlling an equalizer receiving the output of an unknown system in order to produce a desired response for recovering the input to said system are characterized by iteratively adjusting the equalizer such that the unknown system combined with the equalizer behaves essentially as a linear system whose (t, n) taps, for some combinations of t and n, are iteratively adjusted according to the following rule: where s t,n denotes the (t, n) tap before the iteration, S t,n ′ denotes the (t, n) tap after the iteration, I is a preselected integer greater then or equal to one, α i i = 1, 2...I are preselected scalars that may vary from iteration to iteration, and p i ,q i i = 1, 2,...I are preselected non-negative integers such that p i + q i ≧2.

Abstract: A method and apparatus for sharpening signal peaks in a signal representing the distribution of biological or chemical components of a mixture separated by a chromatographic technique such as, but not limited to, electrophoresis. A key step in the method is the use of a blind deconvolution technique, presently embodied as homomorphic filtering, to reduce the contribution of a blurring function to the signal encoding the peaks of the distribution. The invention further includes steps and apparatus directed to determination of a nucleotide sequence from a set of four such signals representing DNA sequence data derived by electrophoretic means.

Abstract: Blind adaptive channel equalizers are important devices to remove channel distortion in high data-rate, bandlimited digital communication systems when the transmission of a training sequence is impractical or very costly. Traditional blind equalization algorithms adapt the equalizer parameters to minimize some specially designed non-MSE cost functions. These algorithms can experience local convergence problems and can thereby result in insufficient or no removal of channel distortion. We present a new quadrature amplitude modulated blind equalization scheme that is globally convergent in the equalizer parameter space to a compact set containing the desired ideal equalizer parameter setting. Our new algorithm is based on a convex cost function and a linear constraint on the equalizer parameters. For a generic class of channels, this new algorithm results in the equalizer parameter convergence to a unique global minimum achieving intersymbol interference suppression and carrier phase error removal. Different implementation approaches are assessed and simulation results are shown to confirm the theoretical global convergence of the new algorithm.

Abstract: The properties of the minimum H/sub infinity /-norm filtering estimation error are investigated, and the relation between the optimal estimator and the equalizing solution to the standard H/sub infinity /-minimization problem is discussed. The optimal estimation method is applied in the multivariable deconvolution problem. A simple deconvolution filter of minimum order which minimizes the H/sub infinity /-norm of the deconvolution error is obtained. The proposed methods of optimal estimation and deconvolution are useful in cases where the statistics of the disturbance and the noise signals is not completely known, or in cases where it is required to minimize the maximum singular value of the estimation, or the deconvolution, error problem. >

Abstract: Relationships between minimum entropy deconvolution, developed primarily for geophysics applications, and blind equalization are pointed out It is seen that a large class of existing blind equalization algorithms are directly related to the scale-invariant cost functions used in minimum entropy deconvolution Thus the extensive analyses of these cost functions can be directly applied to blind equalization, including the important asymptotic results of Donoho

Abstract: Real-time deconvolution can be used as a powerful tool for the identification of linear systems in many areas. The availability of high-speed VLSI convolvers/correlators opens possibilities of dealing with this problem digitally. The application of the frequency-domain Van-Cittert closed form as a deconvolution filter which can be implemented with such devices is analyzed. The topics addressed include the choice of the optimum parameter values (scaling constant, and expansion coefficient) in relation to the deconvolution bandwidth, and hence, deconvolution accuracy. It has been found that this technique shows a low sensitivity to the expansion coefficient value, making any repetitive optimization process unnecessary. >

Abstract: A common approach to blind deconvolution of Bernoulli-Gaussian processes consists of performing both signal restoration and hyperparameter identification through maximization of a single generalized likelihood criterion. It is shown on a simple example that the resulting hyperparameter estimates may not converge toward any meaningful value. Therefore, other more reliable approaches should be adopted whenever possible. >

Abstract: : The deconvolution problem is addressed in stages beginning with the interpolation problem when little prior information is available and proceeding to the full deconvolution problem when a great deal of prior information is available. The results of these calculations indicate that good solutions to the deconvolution program are available even when limited prior information is available and that these results overlap those obtained when a great deal of prior information is available. The difference between them is that the use of uninformative priors causes large uncertainties in the estimated signal, while highly informative priors decreases the uncertainties in the signal.

Abstract: A method of measuring impulse responses of rooms will be described which uses time reversed electronic reverberation from a single pulse as the excitation. The room response, recorded on DAT, is decoded by playing the tape back through the reverberator. The output can be heard, recorded, or analyzed. The method improves S/N by 20 dB and can be implemented with approximately 14 multiples/sample on a PC.

Abstract: Stop-and-go adaptation rules that are utilized to improve the blind convergence characteristics of the conventional and sign decision-directed algorithms are proposed and examined. They are based on the Sato- and Godard-type errors, which are utilized in many blind deconvolution applications. The convergence rates achieved by the algorithms with quadrature amplitude modulated signal constellations and nonminimum phase communication channels are compared. Based on a new criterion, the optimal values of the Sato and Godard error parameters are redefined. The optimality of the new parameter values is confirmed by means of computer simulations.

Abstract: Because chaotic signals are potentially useful both in describing physical phenomena and in engineering applications, signal processing algorithms exploiting their unique characteristics are of interest. The authors consider issues pertaining to processing signals in convolutional distortion. Specifically, they discuss the effects of convolutional distortion on two parameters commonly used in the description of chaotic signals-the Lyapunov exponents and the fractal dimension of the attractor. In addition, a blind deconvolution technique based on minimizing a nonlinear prediction error for data generated by one-dimensional chaotic maps is presented. >

Abstract: A deconvolution technique utilized in image restoration is applied to the problem of estimating the scattering function of a communication channel. Under wide sense stationary and uncorrelated scattering (WSSUS) conditions, the expected matched filter output is equal to the two‐dimensional convolution of the scattering function with the ambiguity function of the interrogating waveform. This convolution process introduces a known blur, the ambiguity function of the transmitted signal, which can be partially removed using a constrained iterative deconvolution technique. A preprocessed matched filter output is used to lessen the amount of unwanted additive noise that is incorporated into the deconvolution process. In the no‐constraint case, it is equivalent to the practice of performing a pseudoinversion using a truncated singular value decomposition (SVD). This particular preprocessed image effectively combines the truncated SVD and Van Cittert deconvolution schemes.

Abstract: Abbreviated. Basic aspects of higher-order spectra and some of their uses (D.R. Brillinger). Independent component analysis (P. Comon). Blind deconvolution using higher-order statistics (C.L. Nikias). Applications of higher order statistics in image processing (G. Jacovitti). Signal Modeling and Estimation. On the bispectrum of complex signals (I. Jouny). Complex random variables: A tensorial approach (J.L. Lacoume, M. Gaeta). On the degree of variety of the third-order statistics of stationary stochastic processes (F. Sakaguchi). New theoretical results on the bistatistics of 2-D signals (A.T. Erdem, A.M. Tekalp). On a method for noise generation with a specified set of higher order cumulants (A.G. Constantinides et al.). Inverse Problem and Identification. On identifiability of ARMA models of non-Gaussian processing via cumulant matching (J.K. Tugnait). Adaptive ARMA identification using cumulants (J.A. Rodriguez-Fonollosa, J. Vidal). A fast phase determination method by a single cumulant sample (C.-Y. Chi, J.-Y. Kung). Cross-bicepstrum and cross-tricepstrum approaches to multichannel deconvolution (D.H. Brooks, C.L. Nikias). Blind deconvolution method based on resonance model of wave propagation (R. Makowski). On a wide class of polyspectral inverse problems (A. Lannes et al.). Non-Stationary Signal Analysis. Detection of linear periodically time varying processes using higher order spectra (G.R. Wilson et al.). Applications Modified fourth-order moments in texture recognition (G. Ramponi, S. Carrato). Polyspectral analysis of non-stationary signals: System identification, classification and ambiguity functions (A.V. Dandawate, G.B. Giannakis). Application on higher-order spectra to high-resolution radar measurements (R.D. Pierce). Array Processing and Source Separation. Array processing from third order functions (M.A. Lagunas, G. Vazquez). Blind separation of sources: An algorithm for separation of convolutive mixtures (C. Jutten et al.). Nonlinear System Analysis Response computation for discrete-time nonlinear systems with random inputs (R. Ingenbleek, H. Schwarz). Second order volterra array processor mismatched to the fourth order moments of the jammers (P. Chevalier, B. Pincinbono). Polyspectra. Reconstruction of a sampled signal Fourier transform from its bispectrum (J. Le Roux). Analysis of nonlinear phenomena in space plasmas (N. Lounis et al.). Author index. (A complete list of contents is available on request from the Publisher.)

Abstract: The author proposes a new approach to recursive estimation of the unknown channel parameters and to adaptive blind deconvolution for data communication systems. The problem is addressed in a blind setting, i.e., only the channel output is observed, not the input to it. The proposed recursive parameter estimator is globally convergent, i.e., the parameter estimator converges to the true model regardless of its initialization. Therefore, the blind equalizer designed based upon the estimated channel parameters is also globally convergent. The proposed parameter estimator is based upon a two model decomposition approach: a SEMP (spectrally equivalent minimum phase) system in cascade with an allpass system. The author exploits the fourth-order cumulant statistics, in addition to the usual second-order statistics, of the data. A computer simulation example is also presented using a 4-PAM (pulse amplitude modulation) signal. >

Abstract: Résumé. 2014 En analyse d’image, les données accessibles ne sont généralement pas de support ponctuel, mais convoluées par une fonction de pondération p(x), déterminée par le processus physique du mode de prélèvement. La déconvolution des images est traitée généralement par transformation de Fourier. Il est bien connu que cette approche est inopérante dans le cas de données bruitées après convolution, de données non disponibles à maille régulière et lorsque des données manquantes doivent être interpolées. C’est pourquoi il est préférable de suivre une autre démarche basée sur une procédure d’estimation des données ponctuelles par krigeage déconvoluant. Les limites pratiques de cette méthode peuvent s’exprimer en termes de variance d’estimation (ou encore de rapport signal

Abstract: A precise expression for the deconvolved signal is derived by introducing the transmission factor, which is defined as the factor of the ratio of the deconvolved signal to the desired signal. An optimal deconvolution system is then defined as the system which minimizes the energy of the maximum distortion factor (=1-transmission factor). It is shown by numerical examples that the proposed system gives superior performance compared to the conventional. >

Abstract: A program adapted for use on microcomputers (DCN) has been developed which permits one to perform operations of numerical convolution and deconvolution using polyexponential functions, that are often implemented in pharmacokinetic analysis. The program is written in Microsoft GWBASIC and can be used in personal computers with no modification. The user supplies information relating to the coefficients and exponentials defining the polyexponential equation of the response and weighting functions and the program performs the deconvolution operation by numerical integration using trapezoidal rule and provides numerical and graphic information concerning the input function. The program can be applied to the deconvolution of many linear pharmacokinetic systems and allows one to solve problems related to drug release, absorption, distribution, as well as others. Additionally, the program is able to perform the convolution operation if information about the input and weighting functions and is also able to simulate pharmacokinetic processes. The efficacy of the program was evaluated by comparison with several deconvolution algorithms, in particular that proposed by Veng-Pedersen and Iga.

Abstract: The authors consider an unknown deterministic or nonGaussian nonwhite stochastic signal transmitted through two different unknown LTI mixed phase FIR systems with only noisy observations of the system outputs. The goal is to identify the systems and/or deconvolve the input, to within a magnitude factor and a time delay. The systems must have no zeros on the unit circle and satisfy other mild conditions on the mutual location of their zeros. Previous approaches have been iterative or assumed the input to be stochastic and white or well-separated from the channel impulse response in some sense. A new non-iterative solution is based on the observation that cepstra (calculated via higher order spectra) corresponding to two 'difference' systems which have zeros due to the minimum (or reflected maximum) phase part of the first system and poles due to the second system can be obtained. Via the group delay separated the 'difference' cepstra are into pole and zero parts and thereby the systems and/or signal are reconstructed. >

Abstract: The author proposes an approach to blind deconvolution of Bernoulli-Gaussian processes based upon true maximum-likelihood estimation of fixed-dimension quantities. The maximum likelihood estimator is implemented using a stochastic version of the expectation-maximization (EM) algorithm. Practical results are in accordance with the known behavior of maximum-likelihood estimates, and the algorithm presents a moderate numerical complexity. >