Publications related to Optimized Wavelet Denoising for Self-Similar alpha-Stable Processes

Which Wavelet Bases Are the Best for Image Denoising?

Michaël Unser, Thierry Blu, Florian Luisier

We use a comprehensive set of non-redundant orthogonal wavelet transforms and apply a denoising method called SUREshrink in each individual wavelet subband to denoise images corrupted by additive Gaussian white noise. We show that, for various images and a ...

SPIE2005

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

Michaël Unser, Dimitri Nestor Alice Van De Ville, Thierry Blu

The approximate behavior of wavelets as differential operators is often considered as one of their most fundamental properties. In this paper, we investigate how we can further improve on the wavelet's behavior as differentiator. In particular, we propose ...

SPIE2005

Wavelets on the 2-Hyperboloid

Pierre Vandergheynst, Iva Bogdanova Vandergheynst

We build wavelets on the 2-Hyperboloid. First, we define dilations on the hyperboloid through conic projection. Then, incorporating hyperbolic motions belonging to

SO_0(1,2)

, we define a family of hyperbolic wavelets. The continuous wavelet transform (CW ...

2004

Extended Depth-of-Focus for Multi-Channel Microscopy Images: A Complex Wavelet Approach

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

Microscopy imaging often suffers from limited depth-of-focus. However, the specimen can be “optically sectioned” by moving the object along the optical axis; different areas appear in focus in different images. Extended depth-of-focus is a fusion algorithm ...

IEEE2004

Wavelet-Based fMRI Statistical Analysis and Spatial Interpretation: A Unifying Approach

Michaël Unser, Dimitri Nestor Alice Van De Ville, Thierry Blu

Wavelet-based statistical analysis methods for fMRI are able to detect brain activity without smoothing the data. Typically, the statistical inference is performed in the wavelet domain by testing the t-values of each wavelet coefficient; subsequently, an ...

IEEE2004

Discrete Wavelet Frames on the Sphere

Pierre Vandergheynst, Laurent Jacques, Iva Bogdanova Vandergheynst

In this paper the Continuous Wavelet Transform on the sphere is exploited to build the asociated Discrete Wavelet Frames. First, the half-continuous frames, i.e. frames where the position remains a continuous variable, is presented and then the fully discr ...

EUSIPCO2004

Guest Editorial: Wavelets in Medical Imaging

Michaël Unser

I. Introduction Wavelets are the result of collective efforts that recognized common threads between ideas and concepts that had been independently developed and investigated by distinct research communities. They provide a unifying framework for decompos ...

2003

Wavelets Versus Resels in the Context of fMRI: Establishing the Link with SPM

Michaël Unser, Dimitri Nestor Alice Van De Ville, Thierry Blu

Statistical Parametric Mapping (SPM) is a widely deployed tool for detecting and analyzing brain activity from fMRI data. One of SPM's main features is smoothing the data by a Gaussian filter to increase the SNR. The subsequent statistical inference is bas ...

SPIE2003

Mathematical Properties of the JPEG2000 Wavelet Filters

Michaël Unser, Thierry Blu

The LeGall 5⁄3 and Daubechies 9⁄7 filters have risen to special prominence because they were selected for inclusion in the JPEG2000 standard. Here, we determine their key mathematical features: Riesz bounds, order of approximation, and regularity (Hölder a ...

IEEE2003

Statistical wavelet analysis of functional images of the brain

Functional magnetic resonance imaging (fMRI) is a recent, non-invasive technique that allows the measurement of brain metabolism while a subject is performing specific motor or cognitive tasks. The practical difficulty is that the signal changes are very s ...

EPFL2002

Optimized Wavelet Denoising for Self-Similar alpha-Stable Processes

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Which Wavelet Bases Are the Best for Image Denoising?

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

Wavelets on the 2-Hyperboloid

Extended Depth-of-Focus for Multi-Channel Microscopy Images: A Complex Wavelet Approach

Wavelet-Based fMRI Statistical Analysis and Spatial Interpretation: A Unifying Approach

Discrete Wavelet Frames on the Sphere

Guest Editorial: Wavelets in Medical Imaging

Wavelets Versus Resels in the Context of fMRI: Establishing the Link with SPM

Mathematical Properties of the JPEG2000 Wavelet Filters

Statistical wavelet analysis of functional images of the brain

Guest Editorial: Wavelets in Medical Imaging

Extended Depth-of-Focus for Multi-Channel Microscopy Images: A Complex Wavelet Approach

Statistical wavelet analysis of functional images of the brain

Wavelets on the 2-Hyperboloid

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

Wavelet-Based fMRI Statistical Analysis and Spatial Interpretation: A Unifying Approach

Discrete Wavelet Frames on the Sphere

Wavelets Versus Resels in the Context of fMRI: Establishing the Link with SPM

Mathematical Properties of the JPEG2000 Wavelet Filters

Which Wavelet Bases Are the Best for Image Denoising?