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

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

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

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

A Time-Domain Wavelet-Based Approach for Fluorescence Diffuse Optical Tomography

Michaël Unser, Chandra Sekhar Seelamantula

Purpose: In the context of fluorescence diffuse optical tomography, determining the optimal way to exploit the time-resolved information has been receiving much attention and different features of the time-resolved signals have been introduced. In this art ...

AAPM2010

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Michaël Unser, Dimitri Nestor Alice Van De Ville, Daniel Sage

The monogenic signal is the natural 2-D counterpart of the 1-D analytic signal. We propose to transpose the concept to the wavelet domain by considering a complexified version of the Riesz transform which has the remarkable property of mapping a real-value ...

Institute of Electrical and Electronics Engineers2009

Gabor Wavelet Analysis and the Fractional Hilbert Transform

Michaël Unser, Kunal Narayan Chaudhury

We propose an amplitude-phase representation of the dual-tree complex wavelet transform (DT-ℂWT) which provides an intuitive interpretation of the associated complex wavelet coefficients. The representation, in particular, is based on the shifting action o ...

SPIE2009

Time Resolved Fluorescence Diffuse Optical Tomography Using Multi-Resolution Exponential B-Splines

Michaël Unser, Chandra Sekhar Seelamantula

This paper deals with the problem of time-resolved fluorescence diffuse optical tomography. We propose a new reconstruction scheme based on a multi-resolution approximation of the time-resolved signals. The underlying basis functions are exponential B-spli ...

IEEE2009

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

Michaël Unser, Dimitri Nestor Alice Van De Ville

A distinction is usually made between wavelet bases and wavelet frames. The former are associated with a one-to-one representation of signals, which is somewhat constrained but most efficient computationally. The latter are over-complete, but they offer ad ...

Institute of Electrical and Electronics Engineers2008

The Monogenic Riesz-Laplace Wavelet Transform

Michaël Unser, Dimitri Nestor Alice Van De Ville, Katarina Balac

We introduce a family of real and complex wavelet bases of

L _{ 2 }

(\mathbb{R} ^{ 2 }

) that are directly linked to the Laplace and Riesz operators. The crucial point is that the family is closed with respect to the Riesz transform which maps a re ...

EURASIP2008

Continuous Wavelet Transform on the Hyperboloid

Pierre Vandergheynst, Iva Bogdanova Vandergheynst

In this paper we build a Continuous Wavelet Transform (CWT) on the upper sheet of the 2-hyperboloid

H_+^2

. First, we define a class of suitable dilations on the hyperboloid through conic projection. Then, incorporating hyperbolic motions belonging to $SO ...

2007

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

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Optimized Wavelet Denoising for Self-Similar alpha-Stable Processes

Optimally Localized Wavelets and Smoothing Kernels

A Time-Domain Wavelet-Based Approach for Fluorescence Diffuse Optical Tomography

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Gabor Wavelet Analysis and the Fractional Hilbert Transform

Time Resolved Fluorescence Diffuse Optical Tomography Using Multi-Resolution Exponential B-Splines

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

The Monogenic Riesz-Laplace Wavelet Transform

Continuous Wavelet Transform on the Hyperboloid

A Time-Domain Wavelet-Based Approach for Fluorescence Diffuse Optical Tomography

Gabor Wavelet Analysis and the Fractional Hilbert Transform

Optimized Wavelet Denoising for Self-Similar alpha-Stable Processes

Optimally Localized Wavelets and Smoothing Kernels

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Time Resolved Fluorescence Diffuse Optical Tomography Using Multi-Resolution Exponential B-Splines

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

The Monogenic Riesz-Laplace Wavelet Transform

Continuous Wavelet Transform on the Hyperboloid