We present a general framework for the design and efficient implementation of various types of running (or over-sampled) wavelet transforms (RWT) using polynomial splines. Unlike previous techniques, the proposed algorithms are not necessarily restricted to scales that are powers of two; yet they all achieve the lowest possible complexity : 0(N) per scale, where N is signal length. In particula...

We propose a new framework to extract the activity-related component in the BOLD functional Magnetic Resonance Imaging (fMRI) signal. As opposed to traditional fMRI signal analysis techniques, we do not impose any prior knowledge of the event timing. Instead, our basic assumption is that the activation pattern is a sequence of short and sparsely-distributed stimuli, as is the case in slow event...

Starting from any two compactly supported refinable functions in L2(R) with dilation factor d, we show that it is always possible to construct 2d wavelet functions with compact support such that they generate a pair of dual d-wavelet frames in L2(R). Moreover, the number of vanishing moments of each of these wavelet frames is equal to the approximation order of the dual MRA; this is the highest...

We propose a flexible and efficient wavelet construction for non-uniform B-spline curves and surfaces. The method allows to remove knots in arbitrary order minimizing the displacement of control points when a knot is re-inserted. Geometric detail subtracted from a shape by knot removal is represented by an associated wavelet coefficient replacing one of the control points at a coarser level of ...

In this paper, we study the problem of constructing non-separable band-limited wavelet tight frames, Riesz wavelets and orthonormal wavelets in R and R. We first construct a class of non-separable band-limited refinable functions in low-dimensional Euclidean spaces by using univariate Meyer’s refinable functions along multiple directions defined by classic box-spline direction matrices. These n...

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...

In a few-view or limited-angle computed tomography (CT), where the number of measurements is far fewer than image unknowns, the reconstruction task is an ill-posed problem. We present a spline-based sparse tomographic reconstruction algorithm where content-adaptive patch sparsity is integrated into the reconstruction process. The proposed method leverages closed-form Radon transforms of tensor-...

This paper reports the work on a novel wavelet-based multi-scale filtering application used to generate very smooth subset of profiles known as Class-A curves. The multi-scale representation, based on B-spline wavelets, allows to split a spline curves in terms of a coarser least-square approximation and details coefficients. It raises that non-Class-A curves are determined by geometric imperfec...

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...