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Michaël Unser

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Publications associées (516)

Tip-Seeking Active Contours for Bioimage Segmentation

Michaël Unser, Virginie Sophie Uhlmann

In the present paper, we address the problem of segmenting biological objects featuring corners. The main ingredients of our approach are automated feature-detection methods and mechanisms for introducing kinks in parametric spline snakes. We formulate a n ...

IEEE2015

Steerable PCA for Rotation-Invariant Image Recognition

Michaël Unser, Cédric René Jean Vonesch, Frédéric Stauber

In this paper, we propose a continuous-domain version of principal-component analysis, with the constraint that the underlying family of templates appears at arbitrary orientations. We show that the corresponding principal components are steerable. Our met ...

SIAM2015

Interpretation of Continuous-Time Autoregressive Processes as Random Exponential Splines

Michaël Unser, John Paul Ward, Julien René Pierre Fageot

We consider the class of continuous-time autoregressive (CAR) processes driven by (possibly non-Gaussian) Lévy white noises. When the excitation is an impulsive noise, also known as compound Poisson noise, the associated CAR process is a random non-uniform ...

IEEE2015

Wavelet Statistics of Sparse and Self-Similar Images

Michaël Unser, Emrah Bostan, Julien René Pierre Fageot

It is well documented that natural images are compressible in wavelet bases and tend to exhibit fractal properties. In this paper, we investigate statistical models that mimic these behaviors. We then use our models to make predictions on the statistics of ...

Siam Publications2015

Improved Variational Denoising of Flow Fields with Application to Phase-Contrast MRI Data

Nikolaos Stergiopoulos, Michaël Unser, Emrah Bostan, Orestis Vardoulis, Stamatios Lefkimmiatis

We propose a new variational framework for the problem of reconstructing flow fields from noisy measurements. The formalism is based on regularizers penalizing the singular values of the Jacobian of the field. Specifically, we rely on the nuclear norm. Our ...

IEEE Institute of Electrical and Electronics Engineers2015

Statistical Optimality of Hermite Splines

Michaël Unser, Virginie Sophie Uhlmann, Julien René Pierre Fageot, Harshit Gupta

Hermite splines are commonly used for interpolating data when samples of the derivative are available, in a scheme called Hermite interpolation. Assuming a suitable statistical model, we demonstrate that this method is actually optimal for reconstructing r ...

IEEE2015

Quantitative evaluation of software packages for single-molecule localization microscopy

Michaël Unser, Daniel Sage, Suliana Manley, Hagay Kirshner, Thomas Pengo

The quality of super-resolution images obtained by single-molecule localization microscopy (SMLM) depends largely on the software used to detect and accurately localize point sources. In this work, we focus on the computational aspects of super-resolution ...

Nature Publishing Group2015

Fast live cell imaging at nanometer scale using annihilating filter based low rank Hankel matrix approach

Michaël Unser, Suliana Manley, Lina Carlini

Localization microscopy such as STORM/PALM can achieve a nanometer scale spatial resolution by iteratively localizing fluorescence molecules. It was shown that imaging of densely activated molecules can accelerate temporal resolution which was considered a ...

Spie-Int Soc Optical Engineering2015

Snakes with Tangent-Based Control and Energies for Bioimage Analysis

Michaël Unser, Virginie Sophie Uhlmann, Ricard Delgado Gonzalo

We propose a novel active contour for the analysis of filament-like structures and boundaries—features that traditional snakes based on closed curves have difficulties to delineate. Our method relies on a parametric representation of an open curve involvin ...

IEEE2014

Phase Retrieval by Using Transport-of-Intensity Equation and Differential Interference Contrast Microscopy

Michaël Unser, Daniel Sage, Benjamin Rappaz, Emrah Bostan, Emmanuel Augustin Julien Froustey

We present a variational reconstruction algorithm for the phase-retrieval problem by using the differential interference contrast microscopy. Principally, we rely on the transport-of-intensity equation that specifies the sought phase as the solution of a p ...

IEEE2014

Harmonic Singular Integrals and Steerable Wavelets in $ L _{ 2 } $ $ (\mathbb{R} ^{ d } $ )

Michaël Unser, John Paul Ward

Here we present a method of constructing steerable wavelet frames in

L _{ 2 }

(\mathbb{R} ^{ d }

) that generalizes and unifies previous approaches, including Simoncelli's pyramid and Riesz wavelets. The motivation for steerable wavelets is the nee ...

Elsevier2014

Exponential Hermite Splines For The Analysis Of Biomedical Images

Michaël Unser, Virginie Sophie Uhlmann, Ricard Delgado Gonzalo

We present a new exponential B-spline basis that enables the construction of active contours for the analysis of biomedical images. Our functions generalize the well-known polynomial Hermite B-splines and provide us with a direct control over the tangents ...

Ieee2014

Matched Wavelet-Like Bases for the Decoupling of Sparse Stochastic Processes

Michaël Unser, Pedram Pad

SMAI-SIGMA2014

Approximation Properties Of Sobolev Splines And The Construction Of Compactly Supported Equivalents

Michaël Unser, John Paul Ward

In this paper, we construct compactly supported radial basis functions that satisfy optimal approximation properties. Error estimates are determined by relating these basis functions to the class of Sobolev splines. Furthermore, we derive new rates for app ...

Siam Publications2014

On the Continuity of Characteristic Functionals and Sparse Stochastic Modeling

Michaël Unser, Arash Amini, Julien René Pierre Fageot

The characteristic functional is the infinite-dimensional generalization of the Fourier transform for measures on function spaces. It characterizes the statistical law of the associated stochastic process in the same way as a characteristic function specif ...

Springer Birkhauser2014

Unsupervised Texture Segmentation Using Monogenic Curvelets and the Potts Model

Michaël Unser, Martin Kurt Storath

We present a method for the unsupervised segmentation of textured images using Potts functionals, which are a piecewise-constant variant of the Mumford and Shah functionals. We propose a minimization strategy based on the alternating direction method of mu ...

IEEE2014

VOW: Variance-Optimal Wavelets for the Steerable Pyramid

Michaël Unser, Virginie Sophie Uhlmann, Pedram Pad

We study the issue of localization in the context of isotropic wavelet frames. We define a variance-type measure of localization and propose an algorithm based on calculus of variations to minimize this criterion under the constraint of a tight wavelet fra ...

IEEE2014

Wavelet-Based Identification and Classification of Local Symmetries in Microscopy Images

Michaël Unser, Zsuzsanna Püspöki

We present a method for the identification and classification of local symmetries in biological images. We aim at obtaining a precise estimate of symmetric junctions in a scale and rotation invariant way. The proposed method is template-free, which allows ...

IEEE2014

Atlas-Free Brain Segmentation in 3D Proton-Density-Like MRI Images

Michaël Unser, Daniel Andreas Schmitter, Ricard Delgado Gonzalo

We present a new method for the atlas-free brain segmentation of proton-density-like 3D MRI images. We show how steerable filters can be efficiently combined with parametric spline surfaces to produce a fast and robust 3D brain segmentation algorithm. The ...

IEEE2014

3D high-density localization microscopy using hybrid astigmatic/biplane imaging and sparse image reconstruction

Michaël Unser, Suliana Manley, Seamus John Holden, Lina Carlini

Localization microscopy achieves nanoscale spatial resolution by iterative localization of sparsely activated molecules, which generally leads to a long acquisition time. By implementing advanced algorithms to treat overlapping point spread functions (PSFs ...

Optical Soc Amer2014

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