This paper is concerned with the construction of biorthogonal wavelet bases defined on a union of parametric images of the unit n-cube. These bases are to satisfy certain requirements imposed by applications to a class of operator equations acting on such domains. This covers also elliptic boundary value problems, although this study is primarily motivated by our previous analysis of wavelet me...

Orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide. We show here that under fairly general conditions, exact reconstruction schemes with synthesis filters different from the analysis filters give rise: to two dual Riesz bases of compactly supported wavelets. We give necessary ...

We show that the tensor product B-spline basis and the triangular Bernstein basis are in some sense best conditioned among all nonnegative bases for the spaces of tensor product splines and multivariate polynomials, respectively. We also introduce some new condition numbers which are analogies of component-wise condition numbers for linear systems introduced by Skeel. x

Digital age today has shown increasing reliance on digital media and rapid distribution of digital contents. The issues of piracy and copyright are of immense concern in this exponentially increasing digital revolution. In this paper, authors propose use of bi-orthogonal wavelet transform as an effective tool to address copyright infringement issues. A synergistic combination of bi-orthogonal w...

Fast trigonometric transforms and periodic orthogonal wavelet transforms are essential tools for numerous practical applications. It is very important that fast algorithms work stable in a floating point arithmetic. This survey paper presents recent results on the worst case analysis of roundoff errors occurring in floating point computation of fast Fourier transforms, fast cosine transforms, a...

In the present work we analyze the performance of orthogonal and Biorthogonal wavelet for electrocardiogram (ECG) compression. Both types of wavelets applied on different types of records taken from MIT-BIH database. A thresholding algorithm based on energy packing efficiency of the wavelet coefficients is used to threshold the wavelet coefficients. We divide wavelet coefficients in two groups ...

In recent years, the wavelet-based image denoising techniques mainly focus on the case that uses a single wavelet base. In fact, different wavelet bases can often effectively represents different areas or features of an image. In this paper a new image denoising method using multiple wavelet bases is proposed. First, the noisy image is denoised by various wavelet bases and then a set of the den...