Publications related to Guest Editorial: Wavelets in Medical Imaging

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-Inst Electrical Electronics Engineers Inc2014

Harmonic singular integrals and steerable wavelets in L-2(R-d)

Michaël Unser, John Paul Ward

Here we present a method of constructing steerable wavelet frames in L-2(R-d) that generalizes and unifies previous approaches, including Simoncelli's pyramid and Riesz wavelets. The motivation for steerable wavelets is the need to more accurately account ...

Academic Press Inc Elsevier Science2014

Harmonic Singular Integrals and Steerable Wavelets in $ L _{ 2 } $ $ (\mathbb{R} ^{ d } $ )

Michaël Unser, John Paul Ward

Here we present a method of constructing steerable wavelet frames in

L _{ 2 }

(\mathbb{R} ^{ d }

) that generalizes and unifies previous approaches, including Simoncelli's pyramid and Riesz wavelets. The motivation for steerable wavelets is the nee ...

Elsevier2014

Wavelets: on the virtues and applications of the mathematical microscope

Michaël Unser

The paper provides a short introduction to wavelets and discusses their main applications in microscopy and biological imaging. ...

Wiley-Blackwell2014

Improved temporal resolution for functional studies with reduced number of segments with three-dimensional echo planar imaging

Rolf Gruetter, Tobias Kober, Wietske Van der Zwaag, José Pedro Rebelo Ferreira Marques, Mayur Narsude

PURPOSE: To introduce a new k-space traversal strategy for segmented three-dimensional echo planar imaging (3D EPI) that encodes two partitions per radiofrequency excitation, effectively reducing the number excitations used to acquire a 3D EPI dataset by h ...

Wiley-Blackwell2014

Statistics of Wavelet Coefficients for Sparse Self-Similar Images

Michaël Unser, Julien René Pierre Fageot, Emrah Bostan

We study the statistics of wavelet coefficients of non-Gaussian images, focusing mainly on the behaviour at coarse scales. We assume that an image can be whitened by a fractional Laplacian operator, which is consistent with an

∥ω∥ ^{ -\gamma }

spectral ...

IEEE2014

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

VOW: Variance-Optimal Wavelets for the Steerable Pyramid

Michaël Unser, Virginie Sophie Uhlmann, Pedram Pad

We study the issue of localization in the context of isotropic wavelet frames. We define a variance-type measure of localization and propose an algorithm based on calculus of variations to minimize this criterion under the constraint of a tight wavelet fra ...

IEEE2014

A simple method to denoise ratio images in magnetic resonance imaging

Alexis Roche, Kieran O'Brien

Disclosed is a Magnetic Resonance Imaging method comprising the steps of: generating an MRI sequence designed for acquiring data from an object to be imaged, wherein the MRI sequence is configured for generating at least two different standard images, resp ...

2014

A Unifying Parametric Framework for 2D Steerable Wavelet Transforms

Michaël Unser

We introduce a complete parameterization of the family of two-dimensional steerable wavelets that are polar-separable in the Fourier domain under the constraint of self-reversibility. These wavelets are constructed by multiorder generalized Riesz transform ...

Siam Publications2013

Guest Editorial: Wavelets in Medical Imaging

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

Harmonic singular integrals and steerable wavelets in L-2(R-d)

Harmonic Singular Integrals and Steerable Wavelets in $ L _{ 2 } $ $ (\mathbb{R} ^{ d } $ )

Wavelets: on the virtues and applications of the mathematical microscope

Improved temporal resolution for functional studies with reduced number of segments with three-dimensional echo planar imaging

Statistics of Wavelet Coefficients for Sparse Self-Similar Images

Multiscale Interior Tomography Using 1D Generalized Total Variation

VOW: Variance-Optimal Wavelets for the Steerable Pyramid

A simple method to denoise ratio images in magnetic resonance imaging

A Unifying Parametric Framework for 2D Steerable Wavelet Transforms

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

Harmonic singular integrals and steerable wavelets in L-2(R-d)

Improved temporal resolution for functional studies with reduced number of segments with three-dimensional echo planar imaging

Statistics of Wavelet Coefficients for Sparse Self-Similar Images

Harmonic Singular Integrals and Steerable Wavelets in $ L _{ 2 } $ $ (\mathbb{R} ^{ d } $ )

Wavelets: on the virtues and applications of the mathematical microscope

Multiscale Interior Tomography Using 1D Generalized Total Variation

VOW: Variance-Optimal Wavelets for the Steerable Pyramid

A Unifying Parametric Framework for 2D Steerable Wavelet Transforms

A simple method to denoise ratio images in magnetic resonance imaging