The Gibbs phenomenon refers to the lack of uniform convergence which occurs in many orthogonal basis approximations to piecewise smooth functions. This lack of uniform convergence manifests itself in spurious oscillations near the points of discontinuity and a low order of convergence away from the dis-continuities. In previous work [11,12] we described a numerical procedure for overcoming the ...

A wavelet optimized finite difference (WOFD) method is presented for adaptively solving a class of singularly perturbed elliptic and parabolic problems. The method is based on an interpolating wavelet transform using polynomial interpolation on dyadic grids. Adaptive feature is performed automatically by thresholding the wavelet coefficients. Numerical examples for elliptic and parabolic proble...

Superresolution produces high-quality, high-resolution images from a set of degraded, low-resolution images where relative frame-to-frame motions provide different looks at the scene. Superresolution translates data temporal bandwidth into enhanced spatial resolution. If considered together on a reference grid, given low-resolution data are nonuniformly sampled. However, data from each frame ar...

Recent wavelet research has primarily focused on real-valued wavelet bases. However, complex wavelet bases offer a number of potential advantageous properties. For example, it has been recently suggested that the complex Daubechies wavelet can be made symmetric. However, these papers always imply that if the complex basis has a symmetry property, then it must exhibit linear phase as well. In th...

The objective of the research presented in this paper is to shed light into the benefits of multi-dimensional wavelet-based methodology applied to NMR biomolecular data analysis. Specifically, the emphasis is on noise reduction for enhanced component identification in multi-dimensional mixture regression. The contributions of this research are multi-fold. First, the wavelet-based noise reductio...

During the process of signal testing, it is often exposed to interference and influence of all kinds of noise signal, such as data collection and transmission and so noise may be introduced. So in practical applications, before analysis of the data measured, the need for de-noising processing. The signal denoising is a method for filtering the high frequency noise of the signal and makes the si...

Wavelet based image denoising methods have attracted extensive interests over the last decade. Donoho et. al. [3] first suggested to remove/suppress noise by thresholding of wavelet coefficients. The underlying assumption is simple and intuitive: a wavelet coefficient is treated as noise and set to zero if it is below a preset threshold. Otherwise, the coefficient is kept or slightly modified. ...

Recent wavelet research has primarily focused on real-valued wavelet bases. However, complex wavelet bases ooer a number of potential advantageous properties. For example, it has been recently suggested 1], 2] that the complex Daubechies wavelet can be made symmetric. However, these papers always imply that if the complex basis has a symmetry property then it must exhibit linear phase as well. ...

In this research the wavelet transform was applied to detect clouds and their shadows and subsequently fill out the missing information in a multitemporal set of Aster images of the north area of Ecuador. Wavelet theory is a powerful mathematical tool recently developed for signal processing. Remote sensing images can be considered as a signal. Furthermore, the wavelet transform is related to t...