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Thierry Blu

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Related publications (64)

Sampling Moments and Reconstructing Signals of Finite Rate of Innovation: Shannon Meets Strang-Fix

Martin Vetterli, Pier Luigi Dragotti, Thierry Blu

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, nonuniform splines or piecewise polynomials, and call the number of degrees of freedom per unit ...

Institute of Electrical and Electronics Engineers2007

The SURE-LET Approach to Image Denoising

Thierry Blu, Florian Luisier

We propose a new approach to image denoising, based on the image-domain minimization of an estimate of the mean squared error—Stein's unbiased risk estimate (SURE). Unlike most existing denoising algorithms, using the SURE makes it needless to hypothesize ...

Institute of Electrical and Electronics Engineers2007

Exact Local Reconstruction Algorithms for Signals with Finite Rate of Innovation

Martin Vetterli, Pier Luigi Dragotti, Thierry Blu

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 polynomial or piecewise sinusoidal signals, and call the number of degrees of freedom ...

2006

Sampling and exact reconstruction of bandlimited signals with additive shot noise

Martin Vetterli, Pina Marziliano, Thierry Blu

In this correspondence, we consider sampling continuous-time periodic bandlimited signals which contain additive shot noise. The classical sampling scheme does not perfectly recover these particular nonbandlimited signals but only reconstructs a lowpass fi ...

IEEE2006

3-D Shape Estimation of DNA Molecules from Stereo Cryo-Electron Micro-Graphs Using a Projection-Steerable Snake

Michaël Unser, Thierry Blu, Mathews Jacob

We introduce a three-dimensional (3-D) parametric active contour algorithm for the shape estimation of DNA molecules from stereo cryo-electron micrographs. We estimate the shape by matching the projections of a 3-D global shape model with the micrographs; ...

IEEE2006

Wavelet-Based Detection of Stimulus Responses in Time-Lapse Microscopy

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

Many experimental paradigms in biology aim at studying the response to coordinated stimuli. In dynamic imaging experiments, the observed data is often not straightforward to interpret and not directly measurable in a quantitative fashion. Consequently, the ...

IEEE2006

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

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

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

Surfing the Brain—An Overview of Wavelet-Based Techniques for fMRI Data Analysis

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

The measurement of brain activity in a noninvasive way is an essential element in modern neurosciences. Modalities such as electroencephalography (EEG) and magnetoencephalography (MEG) recently gained interest, but two classical techniques remain predomina ...

Institute of Electrical and Electronics Engineers2006

Complex B-Splines

Michaël Unser, Thierry Blu

We propose a complex generalization of Schoenberg's cardinal splines. To this end, we go back to the Fourier domain definition of the B-splines and extend it to complex-valued degrees. We show that the resulting complex B-splines are piecewise modulated po ...

Elsevier2006

Optimal Interpolation of Fractional Brownian Motion Given Its Noisy Samples

Michaël Unser, Thierry Blu

We consider the problem of estimating a fractional Brownian motion known only from its noisy samples at the integers. We show that the optimal estimator can be expressed using a digital Wiener-like filter followed by a simple time-variant correction accoun ...

IEEE2006

SURE-Based Wavelet Thresholding Integrating Inter-Scale Dependencies

Michaël Unser, Thierry Blu, Florian Luisier

We propose here a new pointwise wavelet thresholding function that incorporates inter-scale dependencies. This non-linear function depends on a set of four linear parameters per subband which are set by minimizing Stein's unbiased MSE estimate (SURE). Our ...

IEEE2006

Generalized Daubechies Wavelets

Michaël Unser, Thierry Blu, Cédric René Jean Vonesch

We present a generalization of the Daubechies wavelet family. The context is that of a non-stationary multiresolution analysis—i.e., a sequence of embedded approximation spaces generated by scaling functions that are not necessarily dilates of one another. ...

IEEE2005

Generalized Smoothing Splines and the Optimal Discretization of the Wiener Filter

Michaël Unser, Thierry Blu

We introduce an extended class of cardinal LL-splines, where L is a pseudo-differential operator satisfying some admissibility conditions. We show that the LL-spline signal interpolation problem is well posed and that its solution is the unique minimizer ...

IEEE2005

Robust Real-Time Segmentation of Images and Videos Using a Smooth-Spline Snake-Based Algorithm

Michaël Unser, Thierry Blu

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

Hexagonal Versus Orthogonal Lattices: A New Comparison Using Approximation Theory

Thierry Blu, Dimitri Nestor Alice Van De Ville

We provide a new comparison between hexagonal and orthogonal lattices, based on approximation theory. For each of the lattices, we select the “natural” spline basis function as generator for a shift-invariant function space; i.e., the tensor-product B-spli ...

IEEE2005

Beyond Interpolation: Optimal Reconstruction by Quasi-Interpolation

Michaël Unser, Thierry Blu

ICIP'05 Best Student Paper Award We investigate the use of quasi-interpolating approximation schemes, to construct an estimate of an unknown function from its given discrete samples. We show theoretically and with practical experiments that such methods pe ...

IEEE2005

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

Cardinal Exponential Splines: Part I—Theory and Filtering Algorithms

Michaël Unser, Thierry Blu

Causal exponentials play a fundamental role in classical system theory. Starting from those elementary building blocks, we propose a complete and self-contained signal processing formulation of exponential splines defined on a uniform grid. We specify the ...

IEEE2005

Compression of ECG as a Signal with Finite Rate of Innovation

Martin Vetterli, Thierry Blu, Yan Hao

Compression of ECG (electrocardiogram) as a signal with finite rate of innovation (FRI) is proposed in this paper. By modelling the ECG signal as the sum of bandlimited and nonuniform linear spline which contains finite rate of innovation (FRI), sampling t ...

IEEE2005

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