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Michaël Unser

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Related publications (516)

A Unified Formulation of Gaussian Versus Sparse Stochastic Processes-Part I: Continuous-Domain Theory

We introduce a general distributional framework that results in a unifying description and characterization of a rich variety of continuous-time stochastic processes. The cornerstone of our approach is an innovation model that is driven by some generalized ...

Ieee-Inst Electrical Electronics Engineers Inc2014

Cardinal Hermite Exponential Splines: Theoretical Insights and Applications to Active Contours

Michaël Unser, Virginie Sophie Uhlmann

Cardinal Hermite exponential spline functions are a generalization of the classical cardinal Hermite polynomial splines. In this work we consider the 4-dimensional space

ε _{ 4 }

= {1, x,

e ^{ \alpha x }

e ^{ -\alpha x }

} with α ∈ $ ℝ ^{ + } ...

SMAI-SIGMA2014

Statistics of Wavelet Coefficients for Sparse Self-Similar Images

Michaël Unser, Emrah Bostan, Julien René Pierre Fageot

We study the statistics of wavelet coefficients of non-Gaussian images, focusing mainly on the behaviour at coarse scales. We assume that an image can be whitened by a fractional Laplacian operator, which is consistent with an

∥ω∥ ^{ -\gamma }

spectral ...

IEEE2014

Multiscale Interior Tomography Using 1D Generalized Total Variation

Michaël Unser, John Paul Ward

We propose a method for accurate and fast reconstruction of the interior of a 2D or 3D tomographic image from its incomplete local Radon transform. Unlike the existing interior tomography work with 2D total variation, the proposed algorithm guarantees exac ...

The University of Utah2014

Sparsity and Infinite Divisibility

Michaël Unser, Arash Amini

We adopt an innovation-driven framework and investigate the sparse/compressible distributions obtained by linearly measuring or expanding continuous-domain stochastic models. Starting from the first principles, we show that all such distributions are neces ...

2014

High-Performance 3D Deconvolution of Fluorescence Micrographs

Michaël Unser, Stamatios Lefkimmiatis

In this work, we describe our approach of combining the most effective ideas and tools developed during the past years to build a variational 3D deconvolution system that can be successfully employed in fluorescence microscopy. In particular, the main comp ...

IEEE2014

FALCON: fast and unbiased reconstruction of high-density super-resolution microscopy data

Michaël Unser, Cédric René Jean Vonesch, Suliana Manley, Hagay Kirshner, Seamus John Holden, Lina Carlini

Super resolution microscopy such as STORM and (F) PALM is now a well known method for biological studies at the nanometer scale. However, conventional imaging schemes based on sparse activation of photo-switchable fluorescent probes have inherently slow te ...

Nature Publishing Group2014

On the Unique Identification of Continuous-Time Autoregressive Models From Sampled Data

Michaël Unser, Hagay Kirshner, John Paul Ward

In this work, we investigate the relationship between continuous-time autoregressive (AR) models and their sampled version. We consider uniform sampling and derive criteria for uniquely determining the continuous-time parameters from sampled data; the mode ...

Ieee-Inst Electrical Electronics Engineers Inc2014

A Unified Formulation of Gaussian Versus Sparse Stochastic Processes-Part II: Discrete-Domain Theory

Michaël Unser, Pouya Dehghani Tafti, Hagay Kirshner, Arash Amini

This paper is devoted to the characterization of an extended family of continuous-time autoregressive moving average (CARMA) processes that are solutions of stochastic differential equations driven by white Levy innovations. These are completely specified ...

Ieee-Inst Electrical Electronics Engineers Inc2014

Variational Justification of Cycle Spinning for Wavelet-Based Solutions of Inverse Problems

Michaël Unser, Ulugbek Kamilov, Emrah Bostan

Cycle spinning is a widely used approach for improving the performance of wavelet-based methods that solve linear inverse problems. Extensive numerical experiments have shown that it significantly improves the quality of the recovered signal without increa ...

IEEE Institute of Electrical and Electronics Engineers2014

Approximate Message Passing With Consistent Parameter Estimation and Applications to Sparse Learning

Michaël Unser, Ulugbek Kamilov

We consider the estimation of an independent and identically distributed (i.i.d.) (possibly non-Gaussian) vector x is an element of R-n from measurements y is an element of R-m obtained by a general cascade model consisting of a known linear transform foll ...

Ieee-Inst Electrical Electronics Engineers Inc2014

Digital Phase Reconstruction via Iterative Solutions of Transport-of-Intensity Equation

Michaël Unser, Emrah Bostan, Stamatios Lefkimmiatis, Emmanuel Augustin Julien Froustey

We develop a variational algorithm for reconstructing phase objects from a series of bright field micrographs. Our mathematical model is based on the transport-of-intensity equation (TIE), which links the phase of a complex field to the axial derivative of ...

Ieee2014

Wavelets: on the virtues and applications of the mathematical microscope

Michaël Unser

The paper provides a short introduction to wavelets and discusses their main applications in microscopy and biological imaging. ...

Wiley-Blackwell2014

Adaptive Image Resizing Based on Continuous-Domain Stochastic Modeling

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

We introduce an adaptive continuous-domain modeling approach to texture and natural images. The continuous-domain image is assumed to be a smooth function, and we embed it in a parameterized Sobolev space. We point out a link between Sobolev spaces and sto ...

Ieee-Inst Electrical Electronics Engineers Inc2014

Hessian Schatten-Norm Regularization for Linear Inverse Problems

Michaël Unser, Stamatios Lefkimmiatis, John Paul Ward

We introduce a novel family of invariant, convex, and non-quadratic functionals that we employ to derive regularized solutions of ill-posed linear inverse imaging problems. The proposed regularizers involve the Schatten norms of the Hessian matrix, which a ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Design Of Steerable Filters For The Detection Of Micro-Particles

Michaël Unser, Cédric René Jean Vonesch, Frédéric Stauber

This paper presents two contributions. We first introduce a continuous-domain version of Principal-Component Analysis (PCA) for designing steerable filters so that they best approximate a given set of image templates. We exploit the fact that steerability ...

IEEE2013

A Unifying Parametric Framework for 2D Steerable Wavelet Transforms

Michaël Unser

We introduce a complete parameterization of the family of two-dimensional steerable wavelets that are polar-separable in the Fourier domain under the constraint of self-reversibility. These wavelets are constructed by multiorder generalized Riesz transform ...

Siam Publications2013

On the Linearity of Bayesian Interpolators for Non-Gaussian Continuous-Time AR(1) Processes

Philippe Thévenaz, Michaël Unser, Arash Amini, John Paul Ward

Bayesian estimation problems involving Gaussian distributions often result in linear estimation techniques. Nevertheless, there are no general statements as to whether the linearity of the Bayesian estimator is restricted to the Gaussian case. The two comm ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Spline-based framework for interactive segmentation in biomedical imaging

Michaël Unser, Ricard Delgado Gonzalo

Active contours constitute a computationally attractive framework for image segmentation. In this paper, we describe a fully parametric design that relies on B-spline bases and is specified by control points on the image. Our technique yields successful se ...

Elsevier Science Inc2013

MAP Estimators for Self-Similar Sparse Stochastic Models

Michaël Unser, Ulugbek Kamilov, Emrah Bostan, Julien René Pierre Fageot

We consider the reconstruction of multi-dimensional signals from noisy samples. The problem is formulated within the framework of the theory of continuous-domain sparse stochastic processes. In particular, we study the fractional Laplacian as the whitening ...

SampTA2013

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