Publications related to Low-Rate Reduced Complexity Image Compression using Directionlets

Local Geometric Transformations in Image Analysis

The characterization of images by geometric features facilitates the precise analysis of the structures found in biological micrographs such as cells, proteins, or tissues. In this thesis, we study image representations that are adapted to local geometric ...

EPFL2016

Maximally Localized Radial Profiles for Tight Steerable Wavelet Frames

Michaël Unser, Virginie Sophie Uhlmann, Pedram Pad

A crucial component of steerable wavelets is the radial profile of the generating function in the frequency domain. In this paper, we present an infinite-dimensional optimization scheme that helps us find the optimal profile for a given criterion over the ...

IEEE2016

Optimized Steerable Wavelets for Texture Analysis of Lung Tissue In 3-D CT: Classification of Usual Interstitial Pneumonia

Michaël Unser, Adrien Raphaël Depeursinge, Pedram Pad

Our aim is to optimize wavelet-based feature extraction for differentiating between the classical versus atypical pattern of usual interstitial pneumonia (UIP) in volumetric CT. Our proposal is to act on the bandwidth of steerable wavelets while maintainin ...

IEEE2015

Wavelet Statistics of Sparse and Self-Similar Images

Michaël Unser, Julien René Pierre Fageot, Emrah Bostan

It is well documented that natural images are compressible in wavelet bases and tend to exhibit fractal properties. In this paper, we investigate statistical models that mimic these behaviors. We then use our models to make predictions on the statistics of ...

Siam Publications2015

Exploiting Prior Knowledge in Compressed Sensing Wireless ECG Systems

Rafael Eduardo Carrillo Rangel

Recent results in telecardiology show that compressed sensing (CS) is a promising tool to lower energy consumption in wireless body area networks for electrocardiogram (ECG) monitoring. However, the performance of current CS-based algorithms, in terms of c ...

2015

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 ...

Springer Heidelberg2015

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 ...

IEEE2015

Quadtree Structured Image Approximation for Denoising and Interpolation

Adam James Scholefield, Pier Luigi Dragotti

The success of many image restoration algorithms is often due to their ability to sparsely describe the original signal. Shukla et al. proposed a compression algorithm, based on a sparse quadtree decomposition model, which could optimally represent piecewi ...

Institute of Electrical and Electronics Engineers2014

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

Low-Rate Reduced Complexity Image Compression using Directionlets

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Local Geometric Transformations in Image Analysis

Maximally Localized Radial Profiles for Tight Steerable Wavelet Frames

Optimized Steerable Wavelets for Texture Analysis of Lung Tissue In 3-D CT: Classification of Usual Interstitial Pneumonia

Wavelet Statistics of Sparse and Self-Similar Images

Exploiting Prior Knowledge in Compressed Sensing Wireless ECG Systems

On multiscale methods in Petrov-Galerkin formulation

Optimal Isotropic Wavelets for Localized Tight Frame Representations

Quadtree Structured Image Approximation for Denoising and Interpolation

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

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

Maximally Localized Radial Profiles for Tight Steerable Wavelet Frames

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

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

Wavelet Statistics of Sparse and Self-Similar Images

Optimal Isotropic Wavelets for Localized Tight Frame Representations

Quadtree Structured Image Approximation for Denoising and Interpolation

Local Geometric Transformations in Image Analysis

Optimized Steerable Wavelets for Texture Analysis of Lung Tissue In 3-D CT: Classification of Usual Interstitial Pneumonia

On multiscale methods in Petrov-Galerkin formulation

Exploiting Prior Knowledge in Compressed Sensing Wireless ECG Systems