Publications related to Multiresolution analysis

Systematic analysis of wavelet denoising methods for neural signal processing

Objective. Among the different approaches for denoising neural signals, wavelet-based methods are widely used due to their ability to reduce in-band noise. All wavelet denoising algorithms have a common structure, but their effectiveness strongly depends o ...

IOP PUBLISHING LTD2020

Multiresolution Subdivision Snakes

Michaël Unser, Daniel Andreas Schmitter, Virginie Sophie Uhlmann, Anaïs Laure Marie-Thérèse Badoual

We present a new family of snakes that satisfy the property of multiresolution by exploiting subdivision schemes. We show in a generic way how to construct such snakes based on an admissible subdivision mask. We derive the necessary energy formulations and ...

2017

Optimized Wavelet Denoising for Self-Similar alpha-Stable Processes

Michaël Unser, Pedram Pad

We investigate the performance of wavelet shrinkage methods for the denoising of symmetric-a-stable (S alpha S) self-similar stochastic processes corrupted by additive white Gaussian noise (AWGN), where a is tied to the sparsity of the process. The wavelet ...

2017

A Multiscale Pyramid Transform for Graph Signals

Pierre Vandergheynst, David Shuman, Mohammadjavad Faraji

Multiscale transforms designed to process analog and discrete-time signals and images cannot be directly applied to analyze high-dimensional data residing on the vertices of a weighted graph, as they do not capture the intrinsic topology of the graph data ...

Institute of Electrical and Electronics Engineers2016

Firedec: a two-channel finite-resolution image deconvolution algorithm

Frédéric Courbin, Pascale Jablonka, Georges Meylan, Malte Tewes, Nicolas Cantale

We present a two-channel deconvolution method that decomposes images into a parametric point-source channel and a pixelized extended-source channel. Based on the central idea of the deconvolution algorithm proposed by Magain et al. (1998, ApJ, 494, 472), t ...

Edp Sciences S A2016

On multiscale methods in Petrov-Galerkin formulation

Patrick Henning

In this work we investigate the advantages of multiscale methods in Petrov-Galerkin (PG) formulation in a general framework. The framework is based on a localized orthogonal decomposition of a high dimensional solution space into a low dimensional multisca ...

Springer2015

Variational Justification of Cycle Spinning for Wavelet-Based Solutions of Inverse Problems

Michaël Unser, Emrah Bostan, Ulugbek Kamilov

Cycle spinning is a widely used approach for improving the performance of wavelet-based methods that solve linear inverse problems. Extensive numerical experiments have shown that it significantly improves the quality of the recovered signal without increa ...

IEEE Institute of Electrical and Electronics Engineers2014

On the Sparsity of Wavelet Coefficients for Signals on Graphs

Pierre Vandergheynst, Benjamin Ricaud, David Shuman

A number of new localized, multiscale transforms have recently been introduced to analyze data residing on weighted graphs. In signal processing tasks such as regularization and compression, much of the power of classical wavelets on the real line is deriv ...

Spie-Int Soc Optical Engineering2013

S2LET: A code to perform fast wavelet analysis on the sphere

Pierre Vandergheynst, Yves Wiaux, Jason Douglas McEwen

We describe S2LET, a fast and robust implementation of the scale-discretised wavelet transform on the sphere. Wavelets are con- structed through a tiling of the harmonic line and can be used to probe spatially localised, scale-depended features of signals ...

2013

Exponential splines and minimal-support bases for curve representation

Michaël Unser, Philippe Thévenaz, Ricard Delgado Gonzalo

Our interest is to characterize the spline-like integer-shift-invariant bases capable of reproducing exponential polynomial curves. We prove that any compact-support function that reproduces a subspace of the exponential polynomials can be expressed as the ...

Elsevier2012

Shift-Invariant and Sampling Spaces Associated With the Fractional Fourier Transform Domain

Ayush Bhandari

Shift-invariant spaces play an important role in sampling theory, multiresolution analysis, and many other areas of signal and image processing. A special class of the shift-invariant spaces is the class of sampling spaces in which functions are determined ...

2012

A multiresolution method for the simulation of sedimentation in inclined channels

Ricardo Esteban Ruiz Baier

An adaptive multiresolution scheme is proposed for the numerical solution of a spatially two-dimensional model of sedimentation of suspensions of small solid particles dispersed in a viscous fluid. This model consists in a version of the Stokes equations f ...

2012

Wavelet Shrinkage With Consistent Cycle Spinning Generalizes Total Variation Denoising

Michaël Unser, Emrah Bostan, Ulugbek Kamilov

We introduce a new wavelet-based method for the implementation of Total-Variation-type denoising. The data term is least-squares, while the regularization term is gradient-based. The particularity of our method is to exploit a link between the discrete gra ...

IEEE Institute of Electrical and Electronics Engineers2012

A multiresolution approximation method for fast explicit model predictive control

Colin Neil Jones

A model predictive control law is given by the solution to a parametric optimization problem that can be pre- computed offline and provides an explicit map from state to control input. In this paper, an algorithm is introduced based on wavelet multiresolut ...

Institute of Electrical and Electronics Engineers2011

Semi-Supervised Learning with Spectral Graph Wavelets

Pierre Vandergheynst, David Shuman, Mohammadjavad Faraji

We consider the transductive learning problem when the labels belong to a continuous space. Through the use of spectral graph wavelets, we explore the benefits of multiresolution analysis on a graph constructed from the labeled and unlabeled data. The spec ...

2011

Optimally Localized Wavelets and Smoothing Kernels

Kunal Narayan Chaudhury

It is well-known that the Gaussian functions and, more generally, their modulations-translations (the Gabor functions) have the unique property of being optimally localized in space and frequency in the sense of Heisenberg's uncertainty principle. In this ...

EPFL2011

Multiscale analysis of high resolution digital elevation models using the wavelet transform

Michaël Kalbermatten

At the end of the nineties the emergence of high resolution (1 m) digital elevation models (DEMs) settled the context of high precision geomorphological analysis. These new elevation models permitted to reveal structures that remained heretofore undetectab ...

EPFL2010

Fast Explicit Nonlinear Model Predictive Control Via Multiresolution Function Approximation with Guaranteed Stability Nonlinear Control Systems

Colin Neil Jones, John Lygeros

In this paper an algorithm for nonlinear explicit model predictive control is introduced based on multiresolution function approximation that returns a low complexity approximate receding horizon control law built on a hierarchy of second order interpolets ...

2010

Adaptive Multiresolution Methods for the Simulation of Waves in Excitable Media

Ricardo Esteban Ruiz Baier

We present fully adaptive multiresolution methods for a class of spatially two-dimensional reaction-diffusion systems which describe excitable media and often give rise to the formation of spiral waves. A novel model ingredient is a strongly degenerate dif ...

Springer Verlag2010

Wavelet Steerability and the Higher-Order Riesz Transform

Michaël Unser, Dimitri Nestor Alice Van De Ville

Our main goal in this paper is to set the foundations of a general continuous-domain framework for designing steerable, reversible signal transformations (a.k.a. frames) in multiple dimensions (d ≥ 2). To that end, we introduce a self-reversible, Nth-order ...

Institute of Electrical and Electronics Engineers2010