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Michaël Unser

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Related publications (506)

Page 5 of 26

Image Denoising in Mixed Poisson-Gaussian Noise

Michaël Unser, Thierry Blu, Florian Luisier

We propose a general methodology (PURE-LET) to design and optimize a wide class of transform-domain thresholding algorithms for denoising images corrupted by mixed Poisson-Gaussian noise. We express the denoising process as a linear expansion of thresholds ...

Institute of Electrical and Electronics Engineers2011

Bona Fide Riesz Projections For Density Estimation

Michaël Unser, Pol del Aguila Pla

The projection of sample measurements onto a reconstruction space represented by a basis on a regular grid is a powerful and simple approach to estimate a probability density function. In this paper, we focus on Riesz bases and propose a projection operato ...

IEEE2022

Optimality of Operator-Like Wavelets for Representing Sparse AR(1) Processes

Michaël Unser, Pedram Pad

The discrete cosine transform (DCT) is known to be asymptotically equivalent to the Karhunen-Loève transform (KLT) of Gaussian first-order auto-regressive (AR(1)) processes. Since being uncorrelated under the Gaussian hypothesis is synonymous with independ ...

IEEE2015

Optimized Steerable Wavelets for Texture Analysis of Lung Tissue In 3-D CT: Classification of Usual Interstitial Pneumonia

Michaël Unser, Adrien Raphaël Depeursinge, Pedram Pad

Our aim is to optimize wavelet-based feature extraction for differentiating between the classical versus atypical pattern of usual interstitial pneumonia (UIP) in volumetric CT. Our proposal is to act on the bandwidth of steerable wavelets while maintainin ...

IEEE2015

Learning of Continuous and Piecewise-Linear Functions With Hessian Total-Variation Regularization

Michaël Unser, Shayan Aziznejad, Joaquim Gonçalves Garcia Barreto Campos

We develop a novel 2D functional learning framework that employs a sparsity-promoting regularization based on second-order derivatives. Motivated by the nature of the regularizer, we restrict the search space to the span of piecewise-linear box splines shi ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

Fractal Modelling And Analysis Of Flow-Field Images

Michaël Unser, Ricard Delgado Gonzalo, Pouya Dehghani Tafti

We introduce stochastic models for flow fields with parameters that dictate the scale-dependent (self-similar) character of the field and control the balance between its rotational vs compressive behaviour. The development of our models is motivated by the ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2010

Solving Continuous-Domain Problems Exactly with Multiresolution B-Splines

Michaël Unser, Julien René Fageot, Thomas Jean Debarre, Harshit Gupta

We propose a discretization method for continuous-domain linear inverse problems with multiple-order total-variation (TV) regularization. It is based on a recent result that proves that such inverse problems have sparse polynomial-spline solutions. Our met ...

IEEE2019

Generalized Smoothing Splines and the Optimal Discretization of the Wiener Filter

Michaël Unser, Thierry Blu

We introduce an extended class of cardinal LL-splines, where L is a pseudo-differential operator satisfying some admissibility conditions. We show that the LL-spline signal interpolation problem is well posed and that its solution is the unique minimizer ...

IEEE2005

Cardinal Exponential Splines: Part II—Think Analog, Act Digital

Michaël Unser

By interpreting the Green-function reproduction property of exponential splines in signal processing terms, we uncover a fundamental relation that connects the impulse responses of allpole analog filters to their discrete counterparts. The link is that the ...

IEEE2005

Graphic: Graph-Based Hierarchical Clustering For Single-Molecule Localization Microscopy

Michaël Unser, Daniel Sage, Shayan Aziznejad

We propose a novel method for the clustering of point-cloud data that originate from single-molecule localization microscopy (SMLM). Our scheme has the ability to infer a hierarchical structure from the data. It takes a particular relevance when quantitati ...

IEEE2021

Learning Approach to Optical Tomography

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

Optical tomography has been widely investigated for biomedical imaging applications. In recent years optical tomography has been combined with digital holography and has been employed to produce high-quality images of phase objects such as cells. In this p ...

Optical Soc Amer2015

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

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

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

DeconvolutionLab2: An Open-Source Software for Deconvolution Microscopy

Michaël Unser, Daniel Sage, Cédric René Jean Vonesch, Ferréol Arnaud Marie Soulez, Laurène Donati

Images in fluorescence microscopy are inherently blurred due to the limit of diffraction of light. The purpose of deconvolution microscopy is to compensate numerically for this degradation. Deconvolution is widely used to restore fine details of 3D biologi ...

2017

Ridges, Neural Networks, and the Radon Transform

Michaël Unser

A ridge is a function that is characterized by a one-dimensional profile (activation) and a multidimensional direction vector. Ridges appear in the theory of neural networks as functional descriptors of the effect of a neuron, with the direction vector bei ...

2023

General Surface Energy for Spinal Cord and Aorta Segmentation

Michaël Unser, Daniel Andreas Schmitter, Virginie Sophie Uhlmann, Harshit Gupta

We present a new surface energy potential for the segmentation of cylindrical objects in 3D medical imaging using parametric spline active contours (a.k.a. spline-snakes). Our energy formulation is based on an optimal steerable surface detector. Thus, we c ...

IEEE2017

Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid

Michaël Unser, Dimitri Nestor Alice Van De Ville

Our aim in this paper is to tighten the link between wavelets, some classical image-processing operators, and David Marr's theory of early vision. The cornerstone of our approach is a new complex wavelet basis that behaves like a smoothed version of the Gr ...

Institute of Electrical and Electronics Engineers2008

Multi-CryoGAN: Reconstruction of Continuous Conformations in Cryo-EM Using Generative Adversarial Networks

Michaël Unser, Harshit Gupta, Thanh Hai Phan, Jaejun Yoo

We propose a deep-learning-based reconstruction method for cryo-electron microscopy (Cryo-EM) that can model multiple conformations of a nonrigid biomolecule in a standalone manner. Cryo-EM produces many noisy projections from separate instances of the sam ...

Springer, Cham2020

Variational Phase Imaging Using the Transport-of-Intensity Equation

Michaël Unser, Daniel Sage, Emrah Bostan, Masih Nilchian, Emmanuel Augustin Julien Froustey

We introduce a variational phase retrieval algorithm for the imaging of transparent objects. Our formalism is based on the transport-of-intensity equation (TIE), which relates the phase of an optical field to the variation of its intensity along the direct ...

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

A New Hybrid Bayesian-Variational Particle Filter With Application To Mitotic Cell Tracking

Michaël Unser, Ricard Delgado Gonzalo

Tracking algorithms are traditionally based on either a variational approach or a Bayesian one. In the variational case, a cost function is established between two consecutive frames and minimized by standard optimization algorithms. In the Bayesian case, ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2011