Publications related to The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

Continuous Wavelet Transform Ridge Extraction for Spectral Interferometry Imaging

The combination of wavelength multiplexing and spectral interferometry allows for the encoding of multidimensional information and its transmission over a mono-dimensional channel; for example, measurements of a surface's topography acquired through a mono ...

SPIE2005

Exponential-Spline Wavelet Bases

Michaël Unser, Ildar Khalidov

We build a multiresolution analysis based on shift-invariant exponential B-spline spaces. We construct the basis functions for these spaces and for their orthogonal complements. This yields a new family of wavelet-like basis functions of

L _{ 2 }

, wit ...

IEEE2005

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

Correspondence principle between spherical and Euclidean wavelets

Pierre Vandergheynst, Yves Wiaux, Laurent Jacques

Wavelets on the sphere are reintroduced and further developed independently of the original group theoretic formalism, in an equivalent, but more straightforward approach. These developments are motivated by the interest of the scale-space analysis of the ...

2005

Generalized Biorthogonal Daubechies Wavelets

Michaël Unser, Thierry Blu, Cédric René Jean Vonesch

We propose a generalization of the Cohen-Daubechies-Feauveau (CDF) and 9⁄7 biorthogonal wavelet families. This is done within the framework of non-stationary multiresolution analysis, which involves a sequence of embedded approximation spaces generated by ...

SPIE2005

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

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

Complex Wavelets for Extended Depth-of-Field: A New Method for the Fusion of Multichannel Microscopy Images

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

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

Wiley-Liss2004

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

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

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

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Continuous Wavelet Transform Ridge Extraction for Spectral Interferometry Imaging

Exponential-Spline Wavelet Bases

Which Wavelet Bases Are the Best for Image Denoising?

Correspondence principle between spherical and Euclidean wavelets

Generalized Biorthogonal Daubechies Wavelets

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

Wavelets on the 2-Hyperboloid

Complex Wavelets for Extended Depth-of-Field: A New Method for the Fusion of Multichannel Microscopy Images

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

Guest Editorial: Wavelets in Medical Imaging

Which Wavelet Bases Are the Best for Image Denoising?

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

Exponential-Spline Wavelet Bases

Generalized Biorthogonal Daubechies Wavelets

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

Correspondence principle between spherical and Euclidean wavelets

Wavelets on the 2-Hyperboloid

Continuous Wavelet Transform Ridge Extraction for Spectral Interferometry Imaging

Complex Wavelets for Extended Depth-of-Field: A New Method for the Fusion of Multichannel Microscopy Images

Guest Editorial: Wavelets in Medical Imaging