Properties determining optimal behavior of continuous analytic wavelet functions are investigated, and wavelet functions nearly obtaining such behavior are identified. This is accomplished through detailed investigation of the generalized Morse wavelets, a highly flexible family of exactly analytic continuous wavelets. The degree of time/frequency localization, the existence of a unique interpr...

In this work we investigate new feature extraction algorithms on the T-ray response of normal human bone cells and human osteosarcoma cells. One of the most promising feature extraction methods is the Discrete Wavelet Transform (DWT). However, the classification accuracy is dependant on the specific wavelet base chosen. Adaptive wavelets circumvent this problem by gradually adapting to the sign...

Wavelets and multiresolution analysis are instrumental for developing ee-cient methods for representing, storing and manipulating functions at various levels of detail. Although alternative methods such as hierarchical quadtrees or pyramidal models have been used to that eeect as well, wavelets have picked up increasing popularity in recent years due to their energy compactness, ee-ciency, and ...

Fault diagnosis of HV circuit break has been investigated extensively as an important device in the field of power system. In view of the shortcoming of the traditional neural network, such as the slow convergence rate and the local minimum easy to form, fault diagnosis method of HV circuit breaker is proposed to remedy the defects of traditional neural network based on wavelets neural. This me...

This paper investigates intra−adaptive wavelets for video coding with frame−adaptive motion−compensated lifted wavelet transforms. With motion−compensated lifted wavelets, the temporal wavelet decomposition operates along motion trajectories. However, valid trajectories for efficient multi−scale filtering have a finite duration in time. This is due to well known effects like occlusions or inacc...

In this article, we study a class of biorthogonal sampling functions in the context of bandlimited wavelets, Meyer type wavelets. Originally raised in the construction of bandlimited wavelets, these sampling functions also possess a similar structure to the scaling functions of wavelets with adjustable bandwidth parameters. In addition, these sampling functions are infinite impulse response (II...

We introduce a complete parameterization of the family of two-dimensional steerable wavelets that are polar-separable in the Fourier domain under the constraint of self-reversibility. These wavelets are constructed by multiorder generalized Riesz transformation of a primary isotropic bandpass pyramid. The backbone of the transform (pyramid) is characterized by a radial frequency profile functio...

In recent years some attempts have been done to relate the RBF with wavelets [1,2] in handling high dimensional multiscale problems. To the author’s knowledge, however, the orthonormal and bi-orthogonal RBF wavelets are still missing in the literature. By using the nonsingular general solution and singular fundamental solution of differential operator [3], recently the present author made some ...