Inna Kozlov

A Wavelet Packet Algorithm for Classification and Detectionof Moving Vehicles

In this paper we propose a robustalgorithm that solves two related problems: 1) Classificationof acoustic signals emitted by different moving vehicles. Therecorded signals have to be assigned to pre-existing categoriesindependently from the recording surrounding conditions. 2) Detectionof the presence of a vehicle in a certain class via analysisof its acoustic signature against the existing database of recordedand processed acoustic signals. To achieve this detection withpractically no false alarms we construct the acoustic signatureof a certain vehicle using the distribution of the energies amongblocks which consist of wavelet packet coefficients. We allowno false alarms in the detection even under severe conditions;for example when the acoustic recording of target object is asuperposition of the acoustics emitted from other vehicles thatbelong to other classes. The proposed algorithm is robust evenunder severe noise and a range of rough surrounding conditions.This technology, which has many algorithmic variations, can beused to solve a wide range of classification and detection problemswhich are based on acoustic processing which are not relatedto vehicles. These have numerous applications.

IDENTIFICATION OF ACOUSTIC SIGNATURES FOR VEHICLES VIA REDUCTION OF DIMENSIONALITY

In this paper we propose a robust algorithm that solves two related problems: (1) Classification of acoustic signals emitted by different moving vehicles. The recorded signals have to be identified to which pre-existing group they belong to independently of the recording surrounding conditions. (2) Detection of the presence of a vehicle in a certain class via analysis of its acoustic signature against the existing database of recorded and processed acoustic signals. To achieve this detection with minimal false alarms we construct the acoustic signature of a certain vehicle using the distribution of the energies among blocks which consist of coefficients of multiscale local cosine transform (LCT) applied in the frequency domain of the acoustic signal. The proposed algorithm is robust even under severe noise and diverse rough surrounding conditions. This is a generic technology, which has many algorithmic variations, can be used to solve wide range of classification and detection problems which are based on...

Wavelet-packet-based algorithm for identification of quasi-periodic signals

We present a generic approach that identifies and differentiates among signals for wide range of problems. Originally our algorithm was developed to detect the presence of a specific vehicle belonging to a certain class via the analysis of the acoustic signals emitted while it is moving. A crucial factor in having a successful detection (no false alarm) is to construct signatures built from characteristic features that enable to discriminate between the class of interest and the residual information such as background. We construct the signatures of certain classes by the distribution of the energies among blocks which consist of wavelet packet coefficients. We developed an efficient procedure for adaptive selection of the characteristic blocks. We modified the CART algorithm in order to utilize it to be a decision unit in our scheme. However, this technology, which has many algorithmic variations, can be used to solve a wide range of classification and detection problems which are based on acoustic processing and, more generally, for classification and detection of signals which have near-periodic structure. We present results of successful application of the properly modified algorithm to detection of early symptoms of arterial hypertension in children via real-time analysis of pulse signals.

Fast Implementation of ℓ1-Greedy Algorithm

We present an algorithm for finding sparse solutions of the system of linear equations A x = b with the rectangular matrix A of size n ×N, where n < N. The algorithm basic constructive block is one iteration of the standard interior-point linear programming algorithm. To find the sparse representation we modify (reweight) each iteration in the spirit of Petukhov (Fast implementation of orthogonal greedy algorithm for tight wavelet frames. Signal Process. 86, 471–479 (2006)). However, the weights are selected according to the l 1-greedy strategy developed in Kozlov and Petukhov (Sparse solutions for underdetermined systems of linear equations. In: Freeden, W., Nashed, M.Z., Sonar, T. (eds.) Handbook of Geomathematics, pp. 1243–1259. Springer, Berlin (2010)). Our algorithm combines computational complexity close to plain l 1-minimization with the significantly higher efficiency of the sparse representations recovery than the reweighted l 1-minimization (Candes et al.: Enhancing sparsity by reweighted l 1 minimization. J. Fourier Anal. Appl. 14, 877–905 (2008) (special issue on sparsity)), approaching the capacity of the l 1-greedy algorithm.

Wavelet-based algorithm for acoustic detection of moving ground and airborne targets

We detect the presence of a vehicle or an air borne target form a certain class via the analysis of its acoustic signature against an existing database of recorded and processed acoustic signals. To achieve this detection with no false alarms we construct the acoustic signatures of certain targets to be found by the distribution of the energies among blocks which consists of wavelet packet coefficients. We developed an efficient procedure for adaptive selection of the characteristic blocks. We modified the CART algorithm in order to utilize it as a decision unit in our scheme. A wide series of field experiments manifested a remarkable efficiency of the algorithm. The detecting had been achieved practically with no false alarms even under severe conditions such a the acoustic recording of sought- after object was a superposition of the acoustics emitted from other targets that belong to other classes. The detection was even immune to severe noisy surroundings.

Interpolation of cones and shape-preserving approximation

In this paper, we present an approach to shape-preserving approximation based on interpolation space theory. In particular, we prove the corresponding approximation result related to the intersection property of the cone of nonnegative functions with respect to the couple (L p ,B p α,∞).