Publications de Thierry Blu | EPFL Graph Search

A New High-Resolution Processing Method for the Deconvolution of Optical Coherence Tomography Signals

We show the feasibility and the potential of a new signal processing algorithm for the high-resolution deconvolution of OCT signals. Our technique relies on the description of the measures in a parametric form, each set of four parameters describing the op ...

IEEE2002

How a Simple Shift Can Significantly Improve the Performance of Linear Interpolation

Michaël Unser, Philippe Thévenaz, Thierry Blu

We present a simple, original method to improve piecewise linear interpolation with uniform knots: We shift the sampling knots by a fixed amount, while enforcing the interpolation property. Thanks to a theoretical analysis, we determine the optimal shift t ...

IEEE2002

3-D Reconstruction of DNA Filaments from Stereo Cryo-Electron Micrographs

Michaël Unser, Thierry Blu, Mathews Jacob

We propose an algorithm for the 3-D reconstruction of DNA filaments from a pair of stereo cryo-electron micrographs. The underlying principle is to specify a 3-D model of a filament—described as a spline curve—and to fit it to the 2-D data using a snake-li ...

IEEE2002

Sampling of Periodic Signals: A Quantitative Error Analysis

Michaël Unser, Thierry Blu, Mathews Jacob

We present an exact expression for the

L _{ 2 }

error that occurs when one approximates a periodic signal in a basis of shifted and scaled versions of a generating function. This formulation is applicable to a wide variety of linear approximation schem ...

IEEE2002

$ l _{ p } $ -Multiresolution Analysis: How to Reduce Ringing and Sparsify the Error

Michaël Unser, Thierry Blu

We propose to design the reduction operator of an image pyramid so as to minimize the approximation error in the

l _{ p }

-sense (not restricted to the usual p=2), where p can take non-integer values. The underlying image model is specified using shift- ...

IEEE2002

Fresnelets—A New Wavelet Basis for Digital Holography

Michaël Unser, Thierry Blu

We present a new class of wavelet bases—Fresnelets—which is obtained by applying the Fresnel transform operator to a wavelet basis of

L _{ 2 }

. The thus constructed wavelet family exhibits properties that are particularly useful for analyzing and proc ...

SPIE2001

A sampling theorem for periodic piecewise polynomial signals

Martin Vetterli, Pina Marziliano, Thierry Blu

We consider the problem of sampling signals which are not bandlimited, but still have a finite number of degrees of freedom per unit of time, such as, for example, piecewise polynomials. We demonstrate that by using an adequate sampling kernel and a sampli ...

2001

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

An Error Analysis for the Sampling of Periodic Signals

Michaël Unser, Thierry Blu, Mathews Jacob

We analyze the representation of periodic signals in a scaling function basis. This representation is sufficiently general to include the widely used approximation schemes like wavelets, splines and Fourier series representation. We derive a closed form ex ...

SampTA2001

A Unifying Approach and Interface for Spline-Based Snakes

Michaël Unser, Thierry Blu, Mathews Jacob

In this paper, we present different solutions for improving spline-based snakes. First, we demonstrate their minimum curvature interpolation property, and use it as an argument to get rid of the explicit smoothness constraint. We also propose a new externa ...

SPIE2001

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A New High-Resolution Processing Method for the Deconvolution of Optical Coherence Tomography Signals

How a Simple Shift Can Significantly Improve the Performance of Linear Interpolation

3-D Reconstruction of DNA Filaments from Stereo Cryo-Electron Micrographs

Sampling of Periodic Signals: A Quantitative Error Analysis

$ l _{ p } $ -Multiresolution Analysis: How to Reduce Ringing and Sparsify the Error

Fresnelets—A New Wavelet Basis for Digital Holography

A sampling theorem for periodic piecewise polynomial signals

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

An Error Analysis for the Sampling of Periodic Signals

A Unifying Approach and Interface for Spline-Based Snakes

A New High-Resolution Processing Method for the Deconvolution of Optical Coherence Tomography Signals

$ l _{ p } $ -Multiresolution Analysis: How to Reduce Ringing and Sparsify the Error

A Unifying Approach and Interface for Spline-Based Snakes

A sampling theorem for periodic piecewise polynomial signals

How a Simple Shift Can Significantly Improve the Performance of Linear Interpolation

3-D Reconstruction of DNA Filaments from Stereo Cryo-Electron Micrographs

Sampling of Periodic Signals: A Quantitative Error Analysis

Fresnelets—A New Wavelet Basis for Digital Holography

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

An Error Analysis for the Sampling of Periodic Signals