Mati Wax

Bio: Mati Wax is an academic researcher from Technion – Israel Institute of Technology. The author has contributed to research in topics: Multipath propagation & Estimator. The author has an hindex of 38, co-authored 94 publications receiving 11499 citations. Previous affiliations of Mati Wax include Stanford University & Massachusetts Institute of Technology.

Detection of signals by information theoretic criteria

Abstract: A new approach is presented to the problem of detecting the number of signals in a multichannel time-series, based on the application of the information theoretic criteria for model selection introduced by Akaike (AIC) and by Schwartz and Rissanen (MDL). Unlike the conventional hypothesis testing based approach, the new approach does not requite any subjective threshold settings; the number of signals is obtained merely by minimizing the AIC or the MDL criteria. Simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented.

On spatial smoothing for direction-of-arrival estimation of coherent signals

Abstract: We present an analysis of a "spatial smoothing" preprocessing scheme, recently suggested by Evans et al, to circumvent problems encountered in direction-of-arrival estimation of fully correlated signals Simulation results that illustrate the performance of this scheme in conjunction with the eigenstructure technique are described

Maximum likelihood localization of multiple sources by alternating projection

Abstract: An algorithm, referred to as APM, for computing the maximum-likelihood estimator of the locations of simple sources in passive sensor arrays is presented. The algorithm is equally applicable to the case of coherent signals and to the case of a single snapshot. The algorithm is iterative; the maximum of the likelihood function is computed by successive approximations. The convergence of the algorithm to the global maximum is demonstrated for a variety of scenarios. The key to this global convergence is the initialization scheme. >

Spatio-temporal spectral analysis by eigenstructure methods

Abstract: This paper presents new algorithms for estimating the spatio-temporal spectrum of the signals received by a passive array. The algorithms are based on the eigenstructure of the covariance and spectral density matrices of the received signals. They allow partial correlation between the sources and thus are applicable to certain kinds of multipath problems. Simulation results that illustrate the performance of the new algorithms are presented.

Detection of the number of coherent signals by the MDL principle

Abstract: An approach is presented to the problem of detecting the number of sources impinging on a passive sensor array that is based on J. Rissanen's (1983) minimum description length (MDL) principle. The approach is applicable to any type of sources, including the case of sources which are fully correlated, referred to as the coherent signals case. Two slightly different detection criteria are derived, both requiring the estimation of the locations of the sources. The first is tailored to the detection problem per se, whereas the second is tailored to the combined detection/estimation problem. Consistency of the two criteria is proved and their performance is demonstrated by computer simulations. >

ESPRIT-estimation of signal parameters via rotational invariance techniques

Abstract: An approach to the general problem of signal parameter estimation is described. The algorithm differs from its predecessor in that a total least-squares rather than a standard least-squares criterion is used. Although discussed in the context of direction-of-arrival estimation, ESPRIT can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise. It exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure. The technique, when applicable, manifests significant performance and computational advantages over previous algorithms such as MEM, Capon's MLM, and MUSIC. >

Magnetoencephalography—theory, instrumentation, and applications to noninvasive studies of the working human brain

Abstract: Magnetoencephalography (MEG) is a noninvasive technique for investigating neuronal activity in the living human brain. The time resolution of the method is better than 1 ms and the spatial discrimination is, under favorable circumstances, 2-3 mm for sources in the cerebral cortex. In MEG studies, the weak 10 fT-1 pT magnetic fields produced by electric currents flowing in neurons are measured with multichannel SQUID (superconducting quantum interference device) gradiometers. The sites in the cerebral cortex that are activated by a stimulus can be found from the detected magnetic-field distribution, provided that appropriate assumptions about the source render the solution of the inverse problem unique. Many interesting properties of the working human brain can be studied, including spontaneous activity and signal processing following external stimuli. For clinical purposes, determination of the locations of epileptic foci is of interest. The authors begin with a general introduction and a short discussion of the neural basis of MEG. The mathematical theory of the method is then explained in detail, followed by a thorough description of MEG instrumentation, data analysis, and practical construction of multi-SQUID devices. Finally, several MEG experiments performed in the authors' laboratory are described, covering studies of evoked responses and of spontaneous activity in both healthy and diseased brains. Many MEG studies by other groups are discussed briefly as well.

Two decades of array signal processing research: the parametric approach

Abstract: The quintessential goal of sensor array signal processing is the estimation of parameters by fusing temporal and spatial information, captured via sampling a wavefield with a set of judiciously placed antenna sensors. The wavefield is assumed to be generated by a finite number of emitters, and contains information about signal parameters characterizing the emitters. A review of the area of array processing is given. The focus is on parameter estimation methods, and many relevant problems are only briefly mentioned. We emphasize the relatively more recent subspace-based methods in relation to beamforming. The article consists of background material and of the basic problem formulation. Then we introduce spectral-based algorithmic solutions to the signal parameter estimation problem. We contrast these suboptimal solutions to parametric methods. Techniques derived from maximum likelihood principles as well as geometric arguments are covered. Later, a number of more specialized research topics are briefly reviewed. Then, we look at a number of real-world problems for which sensor array processing methods have been applied. We also include an example with real experimental data involving closely spaced emitters and highly correlated signals, as well as a manufacturing application example.

An Introduction to Kolmogorov Complexity and Its Applications

Abstract: The book is outstanding and admirable in many respects. ... is necessary reading for all kinds of readers from undergraduate students to top authorities in the field. Journal of Symbolic Logic Written by two experts in the field, this is the only comprehensive and unified treatment of the central ideas and their applications of Kolmogorov complexity. The book presents a thorough treatment of the subject with a wide range of illustrative applications. Such applications include the randomness of finite objects or infinite sequences, Martin-Loef tests for randomness, information theory, computational learning theory, the complexity of algorithms, and the thermodynamics of computing. It will be ideal for advanced undergraduate students, graduate students, and researchers in computer science, mathematics, cognitive sciences, philosophy, artificial intelligence, statistics, and physics. The book is self-contained in that it contains the basic requirements from mathematics and computer science. Included are also numerous problem sets, comments, source references, and hints to solutions of problems. New topics in this edition include Omega numbers, KolmogorovLoveland randomness, universal learning, communication complexity, Kolmogorov's random graphs, time-limited universal distribution, Shannon information and others.

Detection of signals by information theoretic criteria

Abstract: A new approach is presented to the problem of detecting the number of signals in a multichannel time-series, based on the application of the information theoretic criteria for model selection introduced by Akaike (AIC) and by Schwartz and Rissanen (MDL). Unlike the conventional hypothesis testing based approach, the new approach does not requite any subjective threshold settings; the number of signals is obtained merely by minimizing the AIC or the MDL criteria. Simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented.