We present a general framework for the design of a mother wavelet best adapted to a specific signal or to a class of signals. The filter’s coefficients are obtained via optimization of a smooth objective function. We develop an unconstrained gradient-based optimization algorithm for a discrete wavelet transform. The algorithm is extended to the joint optimization of the mother wavelet and of th...

Wavelet packets are an effective representation tool for adaptive waveform analysis of a given signal. We first combine the wavelet packet representation with zerotree quantization for image coding. A general zerotree structure is defined which can adapt itself to any arbitrary wavelet packet basis. We then describe an efficient coding algorithm based on this structure. Finally, the hypothesis ...

We discuss features extracted from a wavelet packet decomposition for image classification. Statistical features computed from wavelet packet coefficients are compared to structural features which are derived from an image dependent wavelet packet decomposition subband structure. Primary application area is the classification of pit pattern structures in zoom-endoscopic colon imagery, while res...

future design procedures for civil structures, especially those to be protected from extreme and blast relatedloads, will need to account for temporal evolution of their frequency content. there are, however, several instanceswhere acceleration time histories are required as seismic input. for example, to determine the ultimate resistance andto identify modes of structures’ failure, a nonlinear...

In this study, the fusion of optical and synthetic aperture radar images with wavelet transform was investigated. Images are obtained from Sentinel-1 sentinel-2 satellites. were decomposed by transform. The four main coefficients for different packages up to ten decomposition levels. combined taking maximum, minimum or mean. 1710 Fused all possible combinations in terms packets, levels rules. e...

Studying the dynamics of neural activity via electrical recording, relies on the ability to detect and sort neural spikes recorded from a number of neurons by the same electrode. We suggest the wavelet packets decomposition (WPD) as a tool to analyze neural spikes and extract their main features. The unique quality of the wavelet packets-adaptive coverage of both time and frequency domains usin...

The paper presents a versatile library of analytic and quasi-analytic complex-valued wavelet packets (WPs) which originate from discrete splines arbitrary orders. real parts the WPs are regular spline-based orthonormal designed in [4]. imaginary so-called complementary WPs, which, unlike symmetric they antisymmetric. Tensor products 1D provide diversity 2D oriented multiple directions. computat...