John Paul Ward

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Related publications (30)

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On the Continuous Steering of the Scale of Tight Wavelet Frames

Michaël Unser, Daniel Sage, John Paul Ward, Zsuzsanna Püspöki

In analogy with steerable wavelets, we present a general construction of adaptable tight wavelet frames, with an emphasis on scaling operations. In particular, the derived wavelets can be "dilated" by a procedure comparable to the operation of steering ste ...

SIAM2016

The n-term Approximation of Periodic Generalized Levy Processes

Michaël Unser, Julien René Fageot, John Paul Ward

In this paper, we study the compressibility of random processes and fields, called generalized Levy processes, that are solutions of stochastic differential equations driven by d-dimensional periodic Levy white noises. Our results are based on the estimati ...

2020

Compressibility of Symmetric-α-Stable Processes

Michaël Unser, Julien René Fageot, John Paul Ward

Within a deterministic framework, it is well known that n-term wavelet approximation rates of functions can be deduced from their Besov regularity. We use this principle to determine approximation rates for symmetric-α-stable (SαS) stochastic processes. Fi ...

IEEE2015

Multiscale Interior Tomography Using 1D Generalized Total Variation

Michaël Unser, John Paul Ward

We propose a method for accurate and fast reconstruction of the interior of a 2D or 3D tomographic image from its incomplete local Radon transform. Unlike the existing interior tomography work with 2D total variation, the proposed algorithm guarantees exac ...

The University of Utah2014

Interpretation of Continuous-Time Autoregressive Processes as Random Exponential Splines

Michaël Unser, Julien René Fageot, John Paul Ward

We consider the class of continuous-time autoregressive (CAR) processes driven by (possibly non-Gaussian) Lévy white noises. When the excitation is an impulsive noise, also known as compound Poisson noise, the associated CAR process is a random non-uniform ...

IEEE2015

Interior Tomography Using 1D Generalized Total Variation. Part II: Multiscale Implementation

Michaël Unser, John Paul Ward

To address the classic interior tomography problem where projections at each view extend only to the shadow of a circular region completely interior to the subject being scanned, previously we showed that the exact recovery of two- and three-dimensional pi ...

Siam Publications2015

Fast Detection and Refined Scale Estimation Using Complex Isotropic Wavelets

Michaël Unser, Daniel Sage, John Paul Ward, Zsuzsanna Püspöki

The dyadic scaling in the discrete wavelet transform can lead to a loss of precision, in comparison to the computationally unrealistic continuous wavelet transform. To overcome this obstacle, we propose a novel method to locally scale wavelets between dyad ...

IEEE2015

Rotation Invariance and Directional Sensitivity: Spherical Harmonics versus Radiomics Features

Michaël Unser, Julien René Fageot, John Paul Ward, Adrien Raphaël Depeursinge

We define and investigate the Local Rotation Invariance (LRI) and Directional Sensitivity (DS) of radiomics features. Most of the classical features cannot combine the two properties, which are antagonist in simple designs. We propose texture operators bas ...

SPRINGER INTERNATIONAL PUBLISHING AG2018

Optimal Isotropic Wavelets for Localized Tight Frame Representations

Michaël Unser, John Paul Ward, Pedram Pad

In this letter, we aim to identify the optimal isotropic mother wavelet for a given spatial dimension based on a localization criterion. Within the framework of the calculus of variations, we specify an Euler-Lagrange equation for this problem, and we find ...

IEEE Institute of Electrical and Electronics Engineers2015

Approximation Properties Of Sobolev Splines And The Construction Of Compactly Supported Equivalents

Michaël Unser, John Paul Ward

In this paper, we construct compactly supported radial basis functions that satisfy optimal approximation properties. Error estimates are determined by relating these basis functions to the class of Sobolev splines. Furthermore, we derive new rates for app ...

Siam Publications2014