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Mathematical Properties of the JPEG2000 Wavelet Filters

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Rate Distortion Behavior of Sparse Sources

Martin Vetterli

The rate distortion behavior of sparse memoryless sources is studied. These serve as models of sparse signal representations and facilitate the performance analysis of "sparsifying" transforms like the wavelet transform and nonlinear approximation schemes. ...

Institute of Electrical and Electronics Engineers2012

Wavelet Steerability and the Higher-Order Riesz Transform

Michaël Unser, Dimitri Nestor Alice Van De Ville

Our main goal in this paper is to set the foundations of a general continuous-domain framework for designing steerable, reversible signal transformations (a.k.a. frames) in multiple dimensions (d ≥ 2). To that end, we introduce a self-reversible, Nth-order ...

Institute of Electrical and Electronics Engineers2010

Bit Rate Allocation for Disparity Estimation from Compressed Images

Pascal Frossard, Vijayaraghavan Thirumalai

This paper presents a novel rate allocation scheme to compute the 3D structure of the scene from compressed stereo images, captured by the distributed vision sensor networks. The images captured at different view points are encoded independently with a bal ...

2009

Low-Rate Reduced Complexity Image Compression using Directionlets

Martin Vetterli, Vladan Velisavljevic, Pier Luigi Dragotti

The standard separable two-dimensional (2-D) wavelet transform (WT) has recently achieved a great success in image processing because it provides a sparse representation of smooth images. However, it fails to capture efficiently one-dimensional (1-D) disco ...

2006

WSPM or How to Obtain Statistical Parametric Maps Using Shift-Invariant Wavelet Processing

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

Recently, we have proposed a new framework for detecting brain activity from fMRI data, which is based on the spatial discrete wavelet transform. The standard wavelet-based approach performs a statistical test in the wavelet domain, and therefore fails to ...

IEEE2006

Generalized L-Spline Wavelet Bases

Michaël Unser, Thierry Blu, Ildar Khalidov

We build wavelet-like functions based on a parametrized family of pseudo-differential operators

L _{ v }

that satisfy some admissibility and scalability conditions. The shifts of the generalized B-splines, which are localized versions of the Green func ...

SPIE2005

Directionlets

Vladan Velisavljevic

Efficient representation of geometrical information in images is very important in many image processing areas, including compression, denoising and feature extraction. However, the design of transforms that can capture these geometrical features and repre ...

EPFL2005

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

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

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

Generalized L-Spline Wavelet Bases

Michaël Unser, Thierry Blu, Ildar Khalidov

We build wavelet-like functions based on a parametrized family of pseudo-differential operators

L _{ v }

that satisfy some admissibility and scalability conditions. The shifts of the generalized B-splines, which are localized versions of the Green func ...

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