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Michaël Unser

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Related publications (516)

The Monogenic Riesz-Laplace Wavelet Transform

Michaël Unser, Dimitri Nestor Alice Van De Ville, Katarina Balac

We introduce a family of real and complex wavelet bases of

L _{ 2 }

(\mathbb{R} ^{ 2 }

) that are directly linked to the Laplace and Riesz operators. The crucial point is that the family is closed with respect to the Riesz transform which maps a re ...

EURASIP2008

A fast thresholded landweber algorithm for general wavelet bases: Application to 3D deconvolution microscopy

Michaël Unser, Cédric René Jean Vonesch

Wavelet-domain l(1)-regularization is a promising approach to deconvolution. The corresponding variational problem can be solved using a "thresholded Landweber" (TL) algorithm. While this iterative procedure is simple to implement, it is known to converge ...

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

A Fast Thresholded Landweber Algorithm for Wavelet-Regularized Multidimensional Deconvolution

Michaël Unser, Cédric René Jean Vonesch

We present a fast variational deconvolution algorithm that minimizes a quadratic data term subject to a regularization on the

\ell ^{ 1 }

-norm of the wavelet coefficients of the solution. Previously available methods have essentially consisted in alte ...

IEEE2008

Logarithmic Transformation Technique for Exact Signal Recovery in Frequency-Domain Optical-Coherence Tomography

Michaël Unser, Rainer Leitgeb

We address the problem of exact signal recovery in frequency-domain optical-coherence tomography (FDOCT). The standard technique for tomogram reconstruction is the inverse Fourier transform. However, the inverse Fourier transform is known to yield autocorr ...

SPIE2007

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

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

Consistent Sampling and Signal Recovery

Michaël Unser

An attractive formulation of the sampling problem is based on the principle of a consistent signal reconstruction. The requirement is that the reconstructed signal is indistinguishable from the input in the sense that it yields the exact same measurements. ...

Institute of Electrical and Electronics Engineers2007

User-Friendly Semiautomated Assembly of Accurate Image Mosaics in Microscopy

Philippe Thévenaz, Michaël Unser

We present a semiautomated software solution to the problem of extending the lateral field of view of a classical microscope. The initial requirements are a set of overlapping images, along with their user-provided coarse mosaic. Our solution then refines ...

Wiley-Blackwell2007

Full Motion and Flow Field Recovery from Echo Doppler Data

Michaël Unser, Michael Sühling, Muthuvel Arigovindan

We present a new computational method for reconstructing a vector velocity field from scattered, pulsed-wave ultrasound Doppler data. The main difficulty is that the Doppler measurements are incomplete, for they do only capture the velocity component along ...

Institute of Electrical and Electronics Engineers2007

Fast wavelet regularized image deconvolution

Michaël Unser, Cédric René Jean Vonesch

We present a modified version of the deconvolution algorithm introduced by Figueiredo and Nowak, which leads to a substantial acceleration. The algorithm essentially consists in alternating between a Landweber-type iteration and a wavelet-domain denoising ...

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

Sub-resolution maximum-likelihood based localization of fluorescent nanoparticles in three dimensions

Michaël Unser, François Aguet, Dimitri Nestor Alice Van De Ville

Several recent studies have shown that fluorescent particles can be localized with an accuracy that is well beyond traditional resolution limits. Using a theoretical model of the image formation process that accounts for possible sources of noise, Cramer-R ...

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

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

Regularized interpolation for noisy data

Philippe Thévenaz, Michaël Unser, Sathish Ramani

Interpolation is a vital tool in biomedical signal processing. Although there exists a substantial literature dedicated to noise-free conditions, much less is known in the presence of noise. Here, we document the breakdown of standard interpolation for noi ...

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

Reconstruction of Dynamic PET Data Using Spatio-Temporal Wavelet $ ℓ _{ 1 } $ Regularization

Michaël Unser, Dimitri Nestor Alice Van De Ville, Ildar Khalidov

IEEE2007

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