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Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid

Publications associées (44)

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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

A New Family of Complex Rotation-Covariant Multiresolution Bases in 2D

Michaël Unser, Thierry Blu

We present complex rotation-covariant multiresolution families aimed for image analysis. Since they are complex-valued functions, they provide the important phase information, which is missing in the discrete wavelet transform with real wavelets. Our basis ...

SPIE2003

Framing pyramids

Martin Vetterli, Minh Do

In 1983, Burt and Adelson introduced the Laplacian pyramid (LP) as a multiresolution representation for images. We study the LP using the frame theory, and this reveals that the usual reconstruction is suboptimal. We show that the LP with orthogonal filter ...

2003

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

An Exact Method for Computing the Area Moments of Wavelet and Spline Curves

Michaël Unser, Thierry Blu, Mathews Jacob

We present a method for the exact computation of the moments of a region bounded by a curve represented by a scaling function or wavelet basis. Using Green's Theorem, we show that the computation of the area moments is equivalent to applying a suitable mul ...

IEEE2001

Wavelet Projections for Volume Rendering

Michaël Unser, Martin Vetterli

We extended Gross's method of volume wavelet rendering by computing splats via an orthogonal projection operator. The method decomposes the volume data into a wavelet pyramid representation in the spline domain. The splats of the basis functions are approx ...

EUROGRAPHICS1999

Construction of Fractional Spline Wavelet Bases

Michaël Unser, Thierry Blu

We extend Schoenberg's B-splines to all fractional degrees α > -1/2. These splines are constructed using linear combinations of the integer shifts of the power functions

x _{ + } ^{ \alpha }

(one-sided) or

|x| _{ * } ^{ \alpha }

(symmetric); in eac ...

SPIE1999

Wavelets, Filterbanks, and the Karhunen-Loève Transform

Michaël Unser

Most orthogonal signal decompositions, including block transforms, wavelet transforms, wavelet packets, and perfect reconstruction filterbanks in general, can be represented by a paraunitary system matrix. Here, we consider the general problem of finding t ...

EURASIP1998

Shift-Orthogonal Wavelet Bases

Michaël Unser, Philippe Thévenaz

Shift-orthogonal wavelets are a new type of multiresolution wavelet bases that are orthogonal with respect to translation (or shifts) within one level, but not with respect to dilations across scales. In this paper, we characterize these wavelets and inves ...

IEEE1998

Construction of Fractional Spline Wavelet Bases

Michaël Unser, Thierry Blu

We extend Schoenberg's B-splines to all fractional degrees α > -1/2. These splines are constructed using linear combinations of the integer shifts of the power functions

x _{ + } ^{ \alpha }

(one-sided) or

|x| _{ * } ^{ \alpha }

(symmetric); in eac ...

SPIE1999