We discuss the problem of detecting the location of discontinuities of derivatives of a periodic function, given either finitely many Fourier coefficients of the function, or the samples of the function at uniform or scattered data points. Using the general theory, we develop a class of trigonometric polynomial frames suitable for this purpose. Our methods also help us to analyze the capabiliti...

The dyadic lifting schemes, which generalize Sweldens lifting schemes, have been proposed for custom-design of dyadic and bi-orthogonal wavelets and their duals. Starting with dyadic wavelets and exploiting the control provided in the form of free parameters, one can custom-design dyadic as well as bi-orthogonal wavelets adapted to a particular application. To validate the usefulness of the sch...

We investigate biorthogonal spline wavelets on the interval. We give sufficient and necessary conditions for the reconstruction and decomposition matrices to be sparse. Furthermore, we give numerical estimates for the Riesz stability of such bases. §

In this paper, we propose the cubic semi-orthogonal compactly supported B-spline wavelets as a basis functions for the efficient solution of the second kind Fredholm integral equations system. Properties of these wavelets first presented and these properties are then used to reduce the computation of system of integral equations to some algebraic equations. The exponential convergence rate of t...

We investigate mutually orthogonal spline wavelet spaces on non-uniform partitions of a bounded interval, addressing the existence, uniqueness and construction of bases of minimally supported spline wavelets. The relevant algorithms for decomposition and reconstruction are considered as well as some stability-related questions. In addition, we briefly review the bivariate case for tensor produc...

We introduce a new class of wavelets that behave like a given differential operator L. Our construction is inspired by the derivative-like behavior of classical wavelets. Within our framework, the wavelet coefficients of a signal y are the samples of a smoothed version of L{y}. For a linear system characterized by an operator equation L{y} = x, the operator-like wavelet transform essentially de...

This paper presents a new multiscale curvature-based shape representation technique with application to curve data compression using B-spline wavelets. The evolution of the curve is implemented in the B-spline scale-space, which enjoys a number of advantages over the classical Gaussian scale-space, for instance, the availability of fast algorithms. The B-spline wavelet transforms are used to ef...