Publications related to Optimally Localized Wavelets and Smoothing Kernels

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 } $ $ (\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

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

An optimally concentrated Gabor transform for localized time-frequency components

Benjamin Ricaud

Gabor analysis is one of the most common instances of time-frequency signal analysis. Choosing a suitable window for the Gabor transform of a signal is often a challenge for practical applications, in particular in audio signal processing. Many time-freque ...

Springer2014

On the Relevance of Sparsity for Image Classification

Pascal Fua, Engin Türetken, Vincent Lepetit, Germán González Serrano, Roberto Rigamonti, Matthew Brown, Fethallah Benmansour

In this paper we empirically analyze the importance of sparsifying representations for classification purposes. We focus on those obtained by convolving images with linear filters, which can be either hand designed or learned, and perform extensive experim ...

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

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

Multiscale Centerline Detection by Learning a Scale-Space Distance Transform

Pascal Fua, Vincent Lepetit, Amos Sironi

We propose a robust and accurate method to extract the centerlines and scale of tubular structures in 2D images and 3D volumes. Existing techniques rely either on filters designed to respond to ideal cylindrical structures, which lose accuracy when the lin ...

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

On The Optimality Of Operator-Like Wavelets For Sparse Ar(1) Processes

Michaël Unser, Pedram Pad

Sinusoidal transforms such as the DCT are known to be optimal-that is, asymptotically equivalent to the Karhunen-Loeve transform (KLT)-for the representation of Gaussian stationary processes, including the classical AR(1) processes. While the KLT remains a ...

Ieee2013

Optimally Localized Wavelets and Smoothing Kernels

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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 } $ $ (\mathbb{R} ^{ d } $ )

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

An optimally concentrated Gabor transform for localized time-frequency components

On the Relevance of Sparsity for Image Classification

Wavelets: on the virtues and applications of the mathematical microscope

VOW: Variance-Optimal Wavelets for the Steerable Pyramid

Multiscale Centerline Detection by Learning a Scale-Space Distance Transform

A Unifying Parametric Framework for 2D Steerable Wavelet Transforms

On The Optimality Of Operator-Like Wavelets For Sparse Ar(1) Processes

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

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

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

On the Relevance of Sparsity for Image Classification

A Unifying Parametric Framework for 2D Steerable Wavelet Transforms

An optimally concentrated Gabor transform for localized time-frequency components

On The Optimality Of Operator-Like Wavelets For Sparse Ar(1) Processes

VOW: Variance-Optimal Wavelets for the Steerable Pyramid

Wavelets: on the virtues and applications of the mathematical microscope

Multiscale Centerline Detection by Learning a Scale-Space Distance Transform