Valery A. Zheludev

Wavelet-based acoustic detection of moving vehicles

We propose a robust algorithm to detect the arrival of a vehicle of arbitrary type when other noises are present. It is done via analysis of its acoustic signature against an existing database of recorded and processed acoustic signals to detect the arrival of a vehicle of arbitrary type when other noises are present. To achieve it with minimum number of false alarms, we combine a construction of a training database of acoustic signatures signals emitted by vehicles using the distribution of the energies among blocks of wavelet packet coefficients with a procedure of random search for a near-optimal footprint. The number of false alarms in the detection is minimized even under severe conditions such as: the signals emitted by vehicles of different types differ from each other, whereas the set of non-vehicle recordings (the training database) contains signals emitted by planes, helicopters, wind, speech, steps, etc. The proposed algorithm is robust even when the tested conditions are completely different from the conditions where the training signals were recorded. The proposed technique has many algorithmic variations. For example, it can be used to distinguish among different types of vehicles. The proposed algorithm is a generic solution for process control that is based on a learning phase (training) followed by an automatic real-time detection.

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...

A diffusion framework for detection of moving vehicles

We introduce a novel real-time algorithm for automatic acoustic-based vehicle detection. Commonly, surveillance systems for this task use a microphone that is placed in a target area. The recorded sounds are processed in order to detect vehicles as they pass by. The proposed algorithm uses the wavelet-packet transform in order to extract spatio-temporal characteristic features from the recordings. These features constitute a unique acoustic signature for each of the recordings. A more compact signature is derived by the application of the Diffusion Maps (DM) dimensionality reduction algorithm. A new recording is classified according to its compact acoustic signature in the DM reduced-dimension space. The signature is efficiently obtained via the Geometric Harmonics (GH) algorithm. The introduced algorithm is generic and can be applied to various signal types for solving different detection and classification problems.

A new family of spline-based biorthogonal wavelet transforms and their application to image compression

In this paper. we design a new family of biorthogonal wavelet transforms and describe their applications to still image compression. The wavelet transforms are constructed from various types of interpolatory and quasiinterpolatory splines. The transforms use finite impulse response and infinite impulse response filters that are implemented in a fast lifting mode.

Butterworth wavelet transforms derived from discrete interpolatory splines : recursive implementation

In the paper we present a new family of biorthogonal wavelet transforms and the related library of biorthogonal symmetric waveforms. For the construction we used the interpolatory discrete splines which enabled us to design a library ofperf ect reconstruction 0lter banks. These 0lter banks are related to Butterworth 0lters. The construction is performed in a “lifting” manner. The di5erence from the conventional lifting scheme is that the transforms of a signal are performed via recursive 0ltering with the use of IIR 0lters. These 0lters have linear phase property and the basic waveforms are symmetric. The 0lters allow fast cascade or parallel implementation. We present explicit formulas for construction of wavelets with arbitrary number of vanishing moments. In addition, these 0lters yield perfect frequency resolution. The proposed scheme is based on interpolation and, as such, it involves only samples ofsignals and it does not require any use ofquadrature f ? 2001 Elsevier Science B.V. All rights reserved.

Interpolatory frames in signal space

We present a new family of frames, which are generated by perfect reconstruction filter banks of linear phased filters. The filter banks are based on discrete interpolatory splines and are related to Butterworth filters. Each filter bank contains one interpolatory symmetric low-pass filter and two high-pass filters, one of which is also interpolatory and symmetric. The second high-pass filter is either symmetric or antisymmetric. These filter banks generate the analysis and synthesis scaling functions and pairs of framelets. We introduce the concept of semitight frame. All the analysis waveforms in a tight frame coincide with their synthesis counterparts. In the semitight frame, we can trade the number of vanishing moments between the synthesis and the analysis framelets. We construct dual pairs of frames, where all the waveforms are symmetric and all the framelets have the same number of vanishing moments. Although most of the designed filters are infinite-impulse response (IIR), they allow fast implementation via recursive procedures. The waveforms are well localized in time domain despite their infinite support. The frequency response of the designed filters is flat.

Periodic Splines, Harmonic Analysis, and Wavelets

Abstract. We discuss here wavelets constructed from periodic spline functions based on a new computational technique called spline harmonic analysis (SHA). SHA is a version of harmonic analysis operating in the spaces of periodic splines of defect 1 with equidistant nodes. Discrete Fourier transform is a special case of SHA. The continuous Fourier analysis is the limit case of SHA as the degree of splines involved tends to infinity. Thus, SHA bridges the gap between the discrete and the continuous versions of Fourier analysis. SHA can be regarded as a computational version of the harmonic analysis of continuous periodic functions from discrete noised data. The SHA approach to wavelets yields a tool for constructing a diversity of spline wavelet bases, for a fast implementation of the decomposition of a function into a fitting wavelet representation and its reconstruction. Via this approach we are able to construct wavelet packet bases for refined frequency resolution of signals. In this paper we also present algorithms for digital signal processing by means of spline wavelets and wavelet packets. The algorithms established are embodied in a flexible multitasking software for digital signal processing.

Multiwavelet Frames in Signal Space Originated From Hermite Splines

We present a method for construction of multiwavelet frames for manipulation of discrete signals. The frames are generated by three-channel perfect reconstruction oversampled multifilter banks. The design of the multifilter bankstarts from a pair of interpolatory multifilters. We derive these interpolatory multifilters from the cubic Hermite splines. We use the original preprocessing algorithms, which transform scalar signals into vector arrays that serve as inputs to the oversampled analysis multifilter banks. These preprocessing algorithms do not degrade the approximation accuracy of the transforms of the vectors by multifilter banks. The postprocessing algorithms convert the vector output of the synthesis multifilter banks into scalar signal. The discrete framelets, generated by the designed filter banks, are symmetric and have short support. The analysis framelets have four vanishing moments, whereas the synthesis framelets converge to Hermite splines supported on the interval [-1,1]

Lifting scheme for biorthogonal multiwavelets originated from Hermite splines

We present new multiwavelet transforms of multiplicity 2 for manipulation of discrete-time signals. The transforms are implemented in two phases: (1) pre(post)-processing, which transforms the scalar signal into a vector signal (and back) and (2) wavelet transforms of the vector signal. Both phases are performed in a lifting manner. We use the cubic interpolatory Hermite splines as a predicting aggregate in the vector wavelet transform. We present new pre(post)-processing algorithms that do not degrade the approximation accuracy of the vector wavelet transforms. We describe two types of vector wavelet transforms that are dual to each other but have similar properties and three pre(post)processing algorithms. As a result, we get fast biorthogonal algorithms to transform discrete-time signals that are exact on sampled cubic polynomials. The bases for the transform are symmetric and have short support.