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 ...

A construction paradigm is proposed to refine a class of wavelet bases such that the filter characteristics are enhanced. In particular, it is shown that the entire Mth order B-wavelet family belong to this class. Exploiting some recent work, a fast integral wavelet transform is found for the refined B-wavelet family. Moreover, this refined basis can be placed into the setting of a multiresolut...

Decomposing the wavelet transform in lifting steps allows a simpler implementation of the transform filters and provides the flexibility necessary to satisfy other requirements, e.g., generating non-linear integer-to-integer wavelet transforms. The paper presents a flow-graph approach to the lifting factorization that gives a better insight to the main features of single-phase and two-phase wav...

The paper presents computations of decaying two{dimensional turbulence in an adaptive wavelet basis. At each time step the vorticity is represented by an adaptively selected set of wavelet functions which adjusts to the instantaneous distribution of vorticity. The results of this new algorithm are compared to a classical Fourier method and a Fourier method supplemented with wavelet compression ...

In this paper, we propose image restoration algorithms based on adaptive wavelet–domain statistical models. We present a method to estimate the model parameters from the observations, and solve the restoration problem in orthonormal and translation-invariant wavelet domains. Substantial improvements over previous wavelet–based restoration methods are obtained. The use of a translation-invariant...

In this paper, work on a new wavelet packet basis selection paradigm is reported which emphasizes the crucial role of quantization strategy being used. This paradigm is coupled with a new Markov chain based estimation of the cost of zerotree quantization to develop a progressive wavelet packet image coder which gives better results than its wavelet counterpart.

A continuous wavelet transform, with Morlet wavelets as the basis functions, is used to map speech into the time-frequency domain. Forward and inverse FFT routines are used to implement the wavelet transforms. A coefficient covariance matrix is defined and an Eigenvalue decomposition is used to optimally determine significant wavelet based filters that accurately represent speech and potentiall...

Reversible integer wavelet transforms are increasingly popular in lossless image compression, as evidenced by their use in the recently developed JPEG2000 image coding standard 1]. In this paper, a projection technique is described that exploits non-orthogonality among transform basis vectors to derive nal lifting steps for wavelet transforms. Additionally , projection-based predictions of deta...

An application of a wavelet transform and a Bayesian statistical method to seismic event detection and classiication has been studied using data from the New England region. A wavelet expansion forms a new basis set for picking out, from a data stream, important features of a seismic event: time, energy and predominant period of the rst, peak and last waveforms. From these informative features ...