Publications by Thierry Blu | EPFL Graph Search

Optimal Interpolation of Fractional Brownian Motion Given Its Noisy Samples

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

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

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

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

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

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

Hexagonal Versus Orthogonal Lattices: A New Comparison Using Approximation Theory

Dimitri Nestor Alice Van De Ville, Thierry Blu

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

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

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

The approximate behavior of wavelets as differential operators is often considered as one of their most fundamental properties. In this paper, we investigate how we can further improve on the wavelet's behavior as differentiator. In particular, we propose ...

SPIE2005

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

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Optimal Interpolation of Fractional Brownian Motion Given Its Noisy Samples

SURE-Based Wavelet Thresholding Integrating Inter-Scale Dependencies

Sampling and exact reconstruction of bandlimited signals with additive shot noise

Generalized L-Spline Wavelet Bases

Generalized Biorthogonal Daubechies Wavelets

Generalized Daubechies Wavelets

Beyond Interpolation: Optimal Reconstruction by Quasi-Interpolation

Hexagonal Versus Orthogonal Lattices: A New Comparison Using Approximation Theory

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators

Which Wavelet Bases Are the Best for Image Denoising?

Generalized Biorthogonal Daubechies Wavelets

Optimal Interpolation of Fractional Brownian Motion Given Its Noisy Samples

Sampling and exact reconstruction of bandlimited signals with additive shot noise

SURE-Based Wavelet Thresholding Integrating Inter-Scale Dependencies

Beyond Interpolation: Optimal Reconstruction by Quasi-Interpolation

Generalized L-Spline Wavelet Bases

Generalized Daubechies Wavelets

Hexagonal Versus Orthogonal Lattices: A New Comparison Using Approximation Theory

Which Wavelet Bases Are the Best for Image Denoising?

Semi-Orthogonal Wavelets That Behave like Fractional Differentiators