An adaptive algorithm based on wavelets is proposed for the efficient numerical solution of a control problem governed by a linear parabolic evolution equation. First, the constraints are represented by means of a full weak space-time formulation as a linear system in `2 in wavelet coordinates, following a recent approach by Schwab and Stevenson. Second, a quadratic cost functional involving a ...

A wavelet-based method is proposed to obtain accurate estimates of curves in more than one dimension and of their derivatives. By means of simulation studies, this novel method is compared to another locally-adaptive estimation technique for multidimensional functional data, based on free-knot regression splines. This comparison shows that the proposed method is particularly attractive when the...

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...

This paper presents an efficient algorithm for removing noise in satellite images by combining Wavelet Thresholding, Total Variation in wavelet domain and Bilateral Filter, Joint Bilateral Filter (JBF) in spatial domain. During the first stage, the noisy image is passed through Bilateral Filter(BF) and some amount of noise is reduced but the image becomes blurred, hence adaptive wavelet thresho...

Denoising multidimensional NMR-spectra is a fundamental step in NMR protein structure determination. The state-of-the-art method uses wavelet-denoising, which may suffer when applied to non-stationary signals affected by Gaussian-white-noise mixed with strong impulsive artifacts, like those in multi-dimensional NMR-spectra. Regrettably, Wavelet's performance depends on a combinatorial search of...

A wavelet-based lossy-to-lossless image compression technique with polygon-shaped ROI function is proposed. Firstly, split and mergence algorithms are proposed to separate concave ROIs into smaller convex ROIs. Secondly, row-order scan and an adaptive arithmetic coding are used to encode the pixels in ROIs. Thirdly, a lifting integer wavelet transform is used to decompose the original image in ...

This course gives an introduction to the design of efficient datatypes for adaptive waveletbased applications. It presents some code fragments and benchmark technics useful to learn about the design of sparse data structures and adaptive algorithms. Material and practical examples are given, and they provide good introduction for anyone involved in the development of adaptive applications. An a...

We present a study on wavelet detection methods of neuronal action potentials (APs). Our final goal is to implement the selected algorithms on custom integrated electronics for on-line processing of neural signals; therefore we take real-time computing as a hard specification and silicon area as a price to pay. Using simulated neural signals including APs, we characterize an efficient wavelet m...

A new framework for spatio-temporally adaptive turbulence simulations is proposed. The method is based on a variable-fidelity representation that tightly integrates numerics and modelling of subgrid-scale turbulence and aims to capture the flow physics on a near-optimal adaptive mesh. The integration is achieved by combining hierarchical wavelet-based computational modelling with spatially and ...