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Michaël Unser

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Related publications (516)

Efficient Inversion of Multiple-Scattering Model for Optical Diffraction Tomography

Michaël Unser, Thanh-An Michel Pham, Emmanuel Emilien Louis Soubies

Optical diffraction tomography relies on solving an inverse scattering problem governed by the wave equation. Classical reconstruction algorithms are based on linear approximations of the forward model (Born or Rytov), which limits their applicability to t ...

2017

Multiresolution Subdivision Snakes

Michaël Unser, Daniel Andreas Schmitter, Virginie Sophie Uhlmann, Anaïs Laure Marie-Thérèse Badoual

We present a new family of snakes that satisfy the property of multiresolution by exploiting subdivision schemes. We show in a generic way how to construct such snakes based on an admissible subdivision mask. We derive the necessary energy formulations and ...

2017

Jump-Penalized Least Absolute Values Estimation of Scalar or Circle-Valued Signals

Michaël Unser, Martin Kurt Storath

We study jump-penalized estimators based on least absolute deviations which are often referred to as Potts estimators. They are estimators for a parsimonious piecewise constant representation of noisy data having a noise distribution which has heavier tail ...

Oxford University Press2017

Closed-Form Alignment of Active Surface Models Using Splines

Michaël Unser, Daniel Andreas Schmitter

We propose a new formulation of the active surface model in 3D. Instead of aligning a shape dictionary through the similarity transform, we consider more flexible affine transformations and introduce an alignment method that is unbiased in the sense that i ...

IEEE2017

Convolutional Neural Networks for Inverse Problems in Imaging—A Review

Michaël Unser, Michael Thompson McCann, Kyong Hwan Jin

In this article, we review recent uses of convolutional neural networks (CNNs) to solve inverse problems in imaging. It has recently become feasible to train deep CNNs on large databases of images, and they have shown outstanding performance on object clas ...

IEEE2017

Fast Segmentation from Blurred Data in 3D Fluorescence Microscopy

Michaël Unser, Martin Kurt Storath

We develop a fast algorithm for segmenting 3D images from linear measurements based on the Potts model (or piecewise constant Mumford-Shah model). To that end, we first derive suitable space discretizations of the 3D Potts model, which are capable of deali ...

2017

A Sampling Theory for Non-Decaying Signals

Michaël Unser, Quy Ha Nguyen

The classical assumption in sampling and spline theories is that the input signal is square-integrable, which prevents us from applying such techniques to signals that do not decay or even grow at infinity. In this paper, we develop a sampling theory for m ...

2017

Joint absorption and phase retrieval in grating-based x-ray radiography

Michaël Unser, Emrah Bostan, Masih Nilchian, Mohammad Reza Nilchiyan, Marco Stampanoni

Given the raw absorption and differential phase-contrast images obtained from a grating-based x-ray radiography, we formulate the joint denoising of the absorption image and retrieval of the non-differential phase image as a regularized inverse problem. Th ...

Optical Society of America2016

Slice-by-Slice versus Fully 3D Reconstruction for Parallel-Beam x-Ray Microtomography

Michaël Unser, Masih Nilchian, Michael Thompson McCann

We present a 3D iterative reconstruction method for microtomography, where iterative methods have previously been limited by their high computational cost. Our preliminary results show that it improves reconstruction quality over the traditional slice-by-s ...

OSA2016

A Guided Tour of Selected Image Processing and Analysis Methods for Fluorescence and Electron Microscopy

Michaël Unser

Microscopy imaging, including fluorescence microscopy and electron microscopy, has taken a prominent role in life science research and medicine due to its ability to investigate the 3D interior of live cells and organisms. A long-term research in bio-imagi ...

IEEE2016

Optical Tomographic Image Reconstruction Based on Beam Propagation and Sparse Regularization

Michaël Unser, Cédric René Jean Vonesch, Ulugbek Kamilov, Demetri Psaltis

Optical tomographic imaging requires an accurate forward model as well as regularization to mitigate missing-data artifacts and to suppress noise. Nonlinear forward models can provide more accurate interpretation of the measured data than their linear coun ...

2016

Hermite Snakes with Control of Tangents

Michaël Unser, Virginie Sophie Uhlmann, Julien René Pierre Fageot

We introduce a new model of parametric contours defined in a continuous fashion. Our curve model relies on Hermite spline interpolation and can easily generate curves with sharp discontinuities; it also grants direct access to the tangent at each location. ...

IEEE2016

Characterization of the Solution of Linear Inverse Problems with Generalized TV Regularization

Michaël Unser

Ill-posed inverse problems are often constrained by imposing a bound on the total variation of the solution. Here, we consider a generalized version of total-variation regularization that is tied to some differential operator L. We then show that the gener ...

OSA2016

Representer Theorems for Sparsity-Promoting $ ℓ _{ 1 } $ Regularization

Michaël Unser, Julien René Pierre Fageot, Harshit Gupta

We present a theoretical analysis and comparison of the effect of

ℓ _{ 1 }

versus

ℓ _{ 2 }

regularization for the resolution of ill-posed linear inverse and/or compressed sensing problems. Our formulation covers the most general setting where the s ...

IEEE2016

User-Friendly Image-Based Segmentation and Analysis of Chromosomes

Florian Maria Wurm, Michaël Unser, Lucia Baldi Unser, Virginie Sophie Uhlmann, Ricard Delgado Gonzalo

We designed two efficient and user-friendly tools for the segmentation and analysis of images containing chromosomes or, more generally, rod-shaped elements that are spread on microscopic slides. The segmentation tool allows to automatically extract the pr ...

IEEE2016

Introduction to the Issue on Advanced Signal Processing in Microscopy and Cell Imaging

Michaël Unser

Microscopy imaging, including fluorescence microscopy and electron microscopy, has a prominent role in life science and medical research. During the past two decades, biological imaging has undergone a revolution by way of the development of new microscopy ...

IEEE2016

Learning from Examples in Optical Imaging

Michaël Unser, Cédric René Jean Vonesch, Ulugbek Kamilov, Demetri Psaltis

Imaging systems can be designed using examples and methods similar to the techniques used in deep learning. We describe experimental results demonstrating optical tomography based on the learning approach. ...

OSA2016

Exact Algorithms for $ L ^{ 1 } $ -TV Regularization of Real-Valued or Circle-Valued Signals

Michaël Unser, Martin Kurt Storath

We consider

L ^{ 1 }

-TV regularization of univariate signals with values on the real line or on the unit circle. While the real data space leads to a convex optimization problem, the problem is nonconvex for circle-valued data. In this paper, we deriv ...

SIAM2016

Superresolution with Optically-Motivated Blind Deconvolution

Michaël Unser, Ferréol Arnaud Marie Soulez

We show in this paper that an optically motivated parameterization of the PSF prevents classical degeneracies of the blind deconvolution in widefield fluorescence microscopy and provides a resolution close to SIM. ...

OSA2016

Maximally Localized Radial Profiles for Tight Steerable Wavelet Frames

Michaël Unser, Virginie Sophie Uhlmann, Pedram Pad

A crucial component of steerable wavelets is the radial profile of the generating function in the frequency domain. In this paper, we present an infinite-dimensional optimization scheme that helps us find the optimal profile for a given criterion over the ...

IEEE2016

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