We consider the problem of localizing multiple narrow-band stationary signals using an arbitrary time-varying array such as an array mounted on a moving platform. We assume a Gaussian stochastic model for the received signals and employ the generalized least squares (GLS) estimator to get an asymptotically-efficient estimation of the model parameters. In case the signals are a-priori known to be uncorrelated, this estimator allows one to exploit this prior knowledge to its benefit. For the important case of translational motion of a rigid array, a computationally-efficient spatial-smoothing method is presented. Simulation results confirming the theoretical results are included.

We present a new least-squares-based approach for the joint diagonalization problem arising in blind beamforming. The resulting estimation criterion turns out to coincide with that proposed by Cardoso and Souloumaic (see IEE Proc. F, Radar Signal Process., vol.140, no.6, p.362-70, Dec. 1993) on intuitive grounds, thus establishing the optimality of their criterion in the least-squares (LS) sense.

A new technique for localisation of multiple signals is presented. Unlike existing techniques which require that the whole array be sampled simultaneously and consequently require many receivers, our technique allows us to sample arbitrary subarrays sequentially and consequently significantly reduces the required number of receivers. The estimation method we use in conjunction with this sampling scheme is based on approximating the corresponding maximum likelihood estimator by a computationally simpler generalized least squares (GLS) estimator that is proved to be both consistent and efficient.

A new method for localizing multiple signals in spatially-colored background noise using an arbitrary passive sensor array is presented. The method enables also to exploit prior knowledge that the signals are uncorrelated, in case such information is available, so as to improve the performance and allow localization even if the number of signals exceeds the number of sensors. The estimation is based on the generalized least squares criterion, and is both consistent and efficient. Simulation results confirming the theoretical results are included.

A method for detecting curve segments in a digital image is described. The method takes as input a set of edges, and produces as output the number of and parameters for the segments. The method is robust, requiring no thresholds. In place of thresholds, a model class must be provided. Using the information-theoretic minimum description length (MDL) principle, it evaluates each model in the model class, computing the optimal parameters for that model, and selects the best model as the one that gives the shortest encoding of the data and the model. Typical of such methods, the search space is extremely large. It is shown how the Hough transform (HT) may be used to reduce this search space greatly, yielding an efficient (although suboptimal) search. The result is an algorithm in which MDL overcomes standard problems with the HT, while the HT overcomes problems with MDL, and which produces a pleasing set of line segments.>

Considers the problem of unsupervised multiband image segmentation specifically, using the MDL criterion, an associated complexity measure. According to the MDL principle, the best estimates are those that result in the most compact encoding of the image. An important advantage of such an approach is that it is virtually free of the need to choose arbitrary thresholds, which are typical of many segmentation techniques, and which, in many cases, need to be interactively adjusted in order to get satisfactory results.>

An information-theoretic approach is used to derive a new feature selection criterion capable of detecting features that are totally useless. Since the number of useless features is initially unknown, traditional class-separability and distance measures are not capable of coping with this problem. The useless feature-subset is detected by fitting a probability model to a given training set of classified feature-vectors using the minimum-description-length criterion (MDLC) for model selection. The resulting criterion for the Gaussian case is a simple closed-form expression, having a plausible geometric interpretation, and is proved to be consistent, i.e., it yields the true useless subset with probability 1 as the size of the training set grows to infinity. Simulations show excellent results compared to the cross-validation method and other information-theoretic criteria, even for small-sized training sets.>

The application of J. Rissanen's theory (1986) of stochastic complexity to the problem of features selection in statistical pattern recognition (SPR) is discussed. Stochastic complexity provides a general framework for statistical problems such as coding, prediction, estimation, and classification. A brief review of the SPR paradigm and traditional methods of feature selection is presented, followed by a discussion of the basic of stochastic complexity. Two forms of stochastic complexity, minimum description length and an integral form, are applied to the problem of feature selection. Experimental results using simulated data generated with Gaussian distributions are given and compared with results from cross validation, a traditional technique. The stochastic complexity measures give superior results, as measured by their ability to select subsets of relevant features, as well as probability of error computed based on the selected feature subset.>