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The following linear inverse problem is considered: given a full column rank m n data matrix A and a length m observation vector b, nd the best least squares solution to Ax = b with at most r < n nonzero components. The backward greedy algorithm computes a sparse solution to Ax = b by removing greedily columns from A until r columns are left. A simple implementation based on a QR downdating scheme by Givens rotations is described. The backward greedy algorithm is shown to be optimal for this problem in the sense that it selects the \correct" subset of columns from A if the perturbation of the data vector b is small enough.

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We address the problem of estimating the motion of a wide-band source l i m single passive sensor measurements, for example, estimation of the speed and position of a car moving on a road from the recordding of its acoustic signature at a microphone located next to the noad We present a new computationally efficient method based on a time-varying ARMA model for Doppler-shifted random processes. Unlike previously proposed approaches which rely on a "lccal" periodicity hypothesis for the signal source, or a cyclostationary assumption, our method assumes only that the source is stationary and admits a rational (ARMA) model. The method is tested on synthetic and real acoustic data.

The automatic classification of environmental noise sources from their acoustic signatures recorded at the microphone of a noise monitoring system (NMS) is an active subject of research nowadays. This paper shows how hidden Markov models (HMM's) can be used to build an environmental noise recognition system based on a timefrequency analysis of the noise signal. The performance of the proposed HMM-based approach is evaluated experimentally for the classification of five types of noise events (car, truck, moped, aircraft, train). The HMM-based approach is found to outperform previously proposed classifiers based on the average spectrum of noise event with more than 95% of correct classifications. For comparison, a classification test is performed with human listeners for the same data which shows that the best HMM-based classifier outperforms the "average" human listener who achieves only 91.8% of correct classification for the same task.