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Michaël Unser

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Related publications (516)

Bayesian Estimation for Continuous-Time Sparse Stochastic Processes

Michaël Unser, Ulugbek Kamilov, Emrah Bostan, Arash Amini

We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising) and the signal in-between (interpolation problem). By relying on tools fro ...

Ieee-Inst Electrical Electronics Engineers Inc2013

3D Poisson Microscopy Deconvolution With Hessian Schatten-Norm Regularization

Michaël Unser, Stamatios Lefkimmiatis

Inverse problems with shot noise arise in many modern biomedical imaging applications. The main challenge is to obtain an estimate of the underlying specimen from measurements corrupted by Poisson noise. In this work, we propose an efficient framework for ...

IEEE2013

Detection Of Symmetric Junctions In Biological Images Using 2-D Steerable Wavelet Transforms

Michaël Unser, Cédric René Jean Vonesch

We present a method for designing steerable wavelets that can detect local centers of symmetry in images. Based on this design, we then propose an algorithm for estimating the locations and the orientations of M-fold symmetric junctions in biological micro ...

IEEE2013

Iterative FBP For Improved Reconstruction Of X-Ray Differential Phase-Contrast Tomograms

Michaël Unser, Cédric René Jean Vonesch, Masih Nilchian, Peter Modregger, Marco Stampanoni

X-ray differential phase-contrast tomography is a recently-developed modality for the imaging of low-contrast biological samples. Its mathematical model is based on the first derivative of the Radon transform and the images, in practice, are reconstructed ...

IEEE2013

Autocalibrated Signal Reconstruction From Linear Measurements Using Adaptive Gamp

Michaël Unser, Aurélien Bourquard, Ulugbek Kamilov, Emrah Bostan

In this paper, we reconstruct signals from underdetermined linear measurements where the componentwise gains of the measurement system are unknown a priori. The reconstruction is performed through an adaptation of the message-passing algorithm called adapt ...

Ieee2013

A chemostat array enables the spatio-temporal analysis of the yeast proteome

Felix Naef, Michaël Unser, Nicolas Dénervaud, Sebastian Maerkl, Ricard Delgado Gonzalo, Arun Stephen Rajkumar, Johannes Becker

Observing cellular responses to perturbations is central to generating and testing hypotheses in biology. We developed a massively parallel microchemostat array capable of growing and observing 1,152 yeast-GFP strains on the single-cell level with 20 min t ...

National Academy of Sciences2013

Linear Interpolation Of Biomedical Images Using A Data-Adaptive Kernel

Michaël Unser, Aurélien Bourquard, Hagay Kirshner, John Paul Ward

In this work, we propose a continuous-domain stochastic model that can be applied to image data. This model is autoregressive, and accounts for Gaussian-type as well as for non-Gaussian-type innovations. In order to estimate the corresponding parameters fr ...

IEEE2013

Can Localization Microscopy Benefit From Approximation Theory?

Michaël Unser, Cédric René Jean Vonesch, Hagay Kirshner

We introduce a general and computationally efficient approach to 3-D localization microscopy. The main idea is to construct a continuous-domain representation of the PSF by expanding it in a polynomial B-spline basis. This allows us to fit the PSF to the d ...

IEEE2013

Spatio-Temporal Regularization Of Flow-Fields

Nikolaos Stergiopoulos, Michaël Unser, Pouya Dehghani Tafti, Emrah Bostan, Orestis Vardoulis, Davide Piccini

We introduce a novel variational framework for the regularized reconstruction of time-resolved volumetric flow fields. Our objective functional takes the physical characteristics of the underlying flow into account in both the spatial and the temporal doma ...

IEEE2013

Continuous Localization Using Sparsity Constraints for High-Density Super-Resolution Microscopy

Michaël Unser, Cédric René Jean Vonesch, Hagay Kirshner

Super-resolution localization microscopy relies on sparse activation of photo-switchable probes. Such activation, however, introduces limited temporal resolution. High-density imaging overcomes this limitation by allowing several neighboring probes to be a ...

IEEE2013

Fast Maximum Likelihood High-Density Low-SNR Super-Resolution Localization Microscopy

Michaël Unser, Kyungjin Kim

Localization microscopy such as STORM/PALM achieves the super-resolution by sparsely activating photo-switchable probes. However, to make the activation sparse enough to obtain reconstruction images using conventional algorithms, only small set of probes n ...

SampTA2013

MMSE Estimation of Sparse Levy Processes

Michaël Unser, Ulugbek Kamilov, Arash Amini, Pedram Pad

We investigate a stochastic signal-processing framework for signals with sparse derivatives, where the samples of a Levy process are corrupted by noise. The proposed signal model covers the well-known Brownian motion and piecewise-constant Poisson process; ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Poisson Image Reconstruction With Hessian Schatten-Norm Regularization

Michaël Unser, Stamatios Lefkimmiatis

Poisson inverse problems arise in many modern imaging applications, including biomedical and astronomical ones. The main challenge is to obtain an estimate of the underlying image from a set of measurements degraded by a linear operator and further corrupt ...

Ieee-Inst Electrical Electronics Engineers Inc2013

A Shape-Template Based Two-Stage Corpus Callosum Segmentation Technique for Sagittal Plane T1-Weighted Brain Magnetic Resonance Images

Michaël Unser, Chandra Sekhar Seelamantula

We propose a semi-automatic technique to segment corpus callosum (CC) using a two-stage snake formulation: A restricted affine transform (RAT) constrained snake followed by an unconstrained snake in an iterative fashion. A statistical model is developed to ...

IEEE2013

A Practical Inverse-Problem Approach to Digital Holographic Reconstruction

Christian Depeursinge, Michaël Unser, Nicolas Pavillon, Aurélien Bourquard, Emrah Bostan

In this paper, we propose a new technique for high-quality reconstruction from single digital holographic acquisitions. The unknown complex object field is found as the solution of a nonlinear inverse problem that consists in the minimization of an energy ...

OSA2013

Anisotropic Interpolation of Sparse Generalized Image Samples

Michaël Unser, Aurélien Bourquard

Practical image-acquisition systems are often modeled as a continuous-domain prefilter followed by an ideal sampler, where generalized samples are obtained after convolution with the impulse response of the device. In this paper, our goal is to interpolate ...

Ieee-Inst Electrical Electronics Engineers Inc2013

The Analog Formulation of Sparsity Implies Infinite Divisibility and Rules Out Bernoulli-Gaussian Priors

Michaël Unser, Ulugbek Kamilov, Arash Amini

Motivated by the analog nature of real-world signals, we investigate continuous-time random processes. For this purpose, we consider the stochastic processes that can be whitened by linear transformations and we show that the distribution of their samples ...

Ieee2012

Snakes With an Ellipse-Reproducing Property

Philippe Thévenaz, Michaël Unser, Chandra Sekhar Seelamantula, Ricard Delgado Gonzalo

We present a new class of continuously defined parametric snakes using a special kind of exponential splines as basis functions. We have enforced our bases to have the shortest possible support subject to some design constraints to maximize efficiency. Whi ...

IEEE2012

Bi-Exponential Edge-Preserving Smoother

Philippe Thévenaz, Michaël Unser, Daniel Sage

Edge-preserving smoothers need not be taxed by a severe computational cost. We present, in this paper, a lean algorithm that is inspired by the bi-exponential filter and preserves its structure-a pair of one-tap recursions. By a careful but simple local ad ...

Institute of Electrical and Electronics Engineers2012

Exponential splines and minimal-support bases for curve representation

Philippe Thévenaz, Michaël Unser, Ricard Delgado Gonzalo

Our interest is to characterize the spline-like integer-shift-invariant bases capable of reproducing exponential polynomial curves. We prove that any compact-support function that reproduces a subspace of the exponential polynomials can be expressed as the ...

Elsevier2012

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