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Thierry Blu

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Related publications (64)

Multiframe SURE-LET denoising of timelapse fluorescence microscopy images

Michaël Unser, Thierry Blu, Florian Luisier, Saskia Joëlle Delpretti Anex, Sathish Ramani

Due to the random nature of photon emission and the various internal noise sources of the detectors, real timelapse fluorescence microscopy images are usually modeled as the sum of a Poisson process plus some Gaussian white noise. In this paper, we propose ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2008

Shift-Invariant Spaces from Rotation-Covariant Functions

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

We consider shift-invariant multiresolution spaces generated by rotation-covariant functions ρ in

\mathbb{R}^{ 2 }

. To construct corresponding scaling and wavelet functions, ρ has to be localized with an appropriate multiplier, such that the localized ...

Elsevier2008

Sparse Sampling of Signal Innovations

Martin Vetterli, Pina Marziliano, Pier Luigi Dragotti, Thierry Blu, Lionel Coulot

Sparse sampling of continuous-time sparse signals is addressed. In particular, it is shown that sampling at the rate of innovation is possible, in some sense applying Occam's razor to the sampling of sparse signals. The noisy case is analyzed and solved, p ...

Institute of Electrical and Electronics Engineers2008

Nonideal Sampling and Regularization Theory

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

Shannon's sampling theory and its variants provide effective solutions to the problem of reconstructing a signal from its samples in some “shift-invariant” space, which may or may not be bandlimited. In this paper, we present some further justification for ...

IEEE2008

Monte-Carlo SURE: A Black-Box Optimization of Regularization Parameters for General Denoising Algorithms

Michaël Unser, Thierry Blu, Sathish Ramani

We consider the problem of optimizing the parameters of a given denoising algorithm for restoration of a signal corrupted by white Gaussian noise. To achieve this, we propose to minimize Stein's unbiased risk estimate (SURE) which provides a means of asses ...

IEEE2008

Blind optimization of algorithm parameters for signal denoising by Monte-Carlo sure

Michaël Unser, Thierry Blu, Sathish Ramani

We consider the problem of optimizing the parameters of an arbitrary denoising algorithm by minimizing Stein's Unbiased Risk Estimate (SURE) which provides a means of assessing the true mean-squared-error (MSE) purely from the measured data assuming that i ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2008

SURE-LET multichannel image denoising: Undecimated wavelet thresholding

Thierry Blu, Florian Luisier

We propose an extension of the recently devised SURE-LET grayscale denoising approach for multichannel images. Assuming additive Gaussian white noise, the unknown linear parameters of a transform-domain pointwise multichannel thresholding are globally opti ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2008

SURE-LET Multichannel Image Denoising: Interscale Orthonormal Wavelet Thresholding

Thierry Blu, Florian Luisier

We propose a vector/matrix extension of our denoising algorithm initially developed for grayscale images, in order to efficiently process multichannel (e.g., color) images. This work follows our recently published SURE-LET approach where the denoising algo ...

Institute of Electrical and Electronics Engineers2008

Short basis functions for constant-variance interpolation

Philippe Thévenaz, Michaël Unser, Thierry Blu

An interpolation model is a necessary ingredient of intensity-based registration methods. The properties of such a model depend entirely on its basis function, which has been traditionally characterized by features such as its order of approximation and it ...

Spie-Int Soc Optical Engineering, Po Box 10, Bellingham, Wa 98227-0010 Usa2008

Fast Computation of Polyharmonic B-Spline Autocorrelation Filters

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

A fast computational method is given for the Fourier transform of the polyharmonic B-spline autocorrelation sequence in d dimensions. The approximation error is exponentially decaying with the number of terms taken into account. The algorithm improves spee ...

IEEE Institute of Electrical and Electronics Engineers2008

Self-Similarity: Part I—Splines and Operators

Michaël Unser, Thierry Blu

The central theme of this pair of papers (Parts I and II in this issue) is self-similarity, which is used as a bridge for connecting splines and fractals. The first part of the investigation is deterministic, and the context is that of L-splines; these are ...

IEEE2007

Generalized Daubechies Wavelet Families

Michaël Unser, Thierry Blu, Cédric René Jean Vonesch

We present a generalization of the orthonormal Daubechies wavelets and of their related biorthogonal flavors (Cohen-Daubechies-Feauveau, 9⁄7). Our fundamental constraint is that the scaling functions should reproduce a predefined set of exponential polynom ...

IEEE2007

Image denoising by pointwise thresholding of the undecimated wavelet coefficients: A global sure optimum

Thierry Blu, Florian Luisier

We devise a new undecimated wavelet thresholding for denoising images corrupted by additive Gaussian white noise. The first key point of our approach is the use of a linearly parameterized pointwise thresholding function. The second key point consists in o ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2007

Wavelet-Based Multi-Resolution Statistics for Optical Imaging Signals: Application to Automated Detection of Odour Activated Glomeruli in the Mouse Olfactory Bulb

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

Optical imaging techniques offer powerful solutions to capture brain networks processing in animals, especially when activity is distributed in functionally distinct spatial domains. Despite the progress in imaging techniques, the standard analysis procedu ...

Elsevier2007

A new technique for high-resolution frequency domain optical coherence tomography

Michaël Unser, Thierry Blu

Frequency domain optical coherence tomography (FDOCT) is a new technique that is well-suited for fast imaging of biological specimens, as well as non-biological objects. The measurements are in the frequency domain, and the objective is to retrieve an arti ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2007

WSPM: Wavelet-Based Statistical Parametric Mapping

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

Recently, we have introduced an integrated framework that combines wavelet-based processing with statistical testing in the spatial domain. In this paper, we propose two important enhancements of the framework. First, we revisit the underlying paradigm; i. ...

Elsevier2007

Self-Similarity: Part II—Optimal Estimation of Fractal Processes

Michaël Unser, Thierry Blu

IEEE2007

A New SURE Approach to Image Denoising: Interscale Orthonormal Wavelet Thresholding

Michaël Unser, Thierry Blu, Florian Luisier

This paper introduces a new approach to orthonormal wavelet image denoising. Instead of postulating a statistical model for the wavelet coefficients, we directly parametrize the denoising process as a sum of elementary nonlinear processes with unknown weig ...

Institute of Electrical and Electronics Engineers2007

Non-iterative exact signal recovery in frequency domain optical coherence tomography

Michaël Unser, Thierry Blu, Rainer Leitgeb

We address the problem of exact signal recovery in frequency domain optical coherence tomography (FDOCT) systems. Our technique relies on the fact that, in a spectral interferometry setup, the intensity of the total signal reflected from the object is smal ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2007

Wavelet-Based Statistical Analysis for Optical Imaging in Mouse Olfactory Bulb

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

Optical imaging is a powerful technique to map brain function in animals. In this study, we consider in vivo optical imaging of the murine olfactory bulb, using an intrinsic signal and a genetically expressed activity reporter fluorescent protein (synaptop ...

IEEE2007

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