Publications by Michaël Unser

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We present a new computational method for reconstructing a vector field from scattered, pulsed-wave ultrasound Doppler data. The main difficulty is that the Doppler measurements are incomplete, for they do only capture the velocity component along the beam ...

We study continuous-domain linear inverse problems that involve a general data-fidelity term and a regularisation term. We consider a regularisation that is formed by the sparsity-promoting total-variation norm, pre-composed with a differential operator th ...

Echo-planar imaging (EPI) is a fast nuclear magnetic resonance imaging (MRI) method. Unfortunately, local magnetic field inhomogeneities induced mainly by the subject's presence cause significant geometrical distortion, predominantly along the phase-encoding direction, which must be undone to allow for meaningful further processing. So far, this aspect has been too often neglected. In this paper, we suggest a new approach using an algorithm specifically developed for the automatic registration of distorted

The 32 telomeres in the budding yeast genome cluster in three to seven perinuclear foci. Although individual telomeres and telomeric foci are in constant motion, preferential juxtaposition of some telomeres has been scored. To examine the principles that g ...

We present a new fast active-contour model (a.k.a. snake) for image segmentation in 3D microscopy. We introduce a parametric design that relies on exponential B-spline bases and allows us to build snakes that are able to reproduce ellipsoids. We design our ...

We propose the use of Flat Metric to assess the performance of reconstruction methods for single-molecule localization microscopy (SMLM) in scenarios where the ground-truth is available. Flat Metric is intimately related to the concept of optimal transport ...

Brightfield microscopy often suffers from limited depth of field, which prevents thick specimens from being imaged entirely in-focus. By optically sectioning the specimen, the in-focus regions can be acquired over multiple images. Extended depth of field m ...

A distinction is usually made between wavelet bases and wavelet frames. The former are associated with a one-to-one representation of signals, which is somewhat constrained but most efficient computationally. The latter are over-complete, but they offer ad ...

We present a new class of wavelet bases—Fresnelets—which is obtained by applying the Fresnel transform operator to a wavelet basis of

L _{ 2 }

. The thus constructed wavelet family exhibits properties that are particularly useful for analyzing and processing optically generated holograms recorded on CCD-arrays. We first investigate the multiresolution properties (translation, dilation) of the Fresnel transform that are needed to construct our new wavelet. We derive a Heisenberg-like uncertainty relation

In recent years, researchers have obtained impressive reconstructions of the refractive index (RI) of biological objects through the combined use of advanced physics (nonlinear forward model) and regularization. Here, we propose an adaptation of these tech ...

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 ...

Due to the random nature of photon emission and the various internal noise sources of the detectors, real timelapse fluorescence microscopy images are usually modeled as the sum of a Poisson process plus some Gaussian white noise. In this paper, we propose ...

We consider the problem of reconstructing a multidimensional and multivariate function ƒ:

ℜ ^{ m }

\rightarrow

ℜ ^{ n }

from the discretely and irregularly sampled responses of q linear shift-invariant filters. Unlike traditional approaches which reconstruct the function in some signal space V, our reconstruction is optimal in the sense of a plausibility criterion J. The reconstruction is either consistent with the measures, or minimizes the consistence error. There is no band-limiting restriction f

Determining the structure and composition of macromolecular assemblies is a major challenge in biology. Here we describe ultrastructure expansion microscopy (U-ExM), an extension of expansion microscopy that allows the visualization of preserved ultrastruc ...

To address the classic interior tomography problem where projections at each view extend only to the shadow of a circular region completely interior to the subject being scanned, previously we showed that the exact recovery of two- and three-dimensional pi ...

This chapter describes tools and techniques that facilitate a gentle introduction to fascinating concepts in digital image processing from four leading universities. Equipped with informative visualizations and a user-friendly interfaces, these modules are currently being used effectively in a classroom environment for teaching DIP at many universities across the world.

One of the ongoing challenges in single particle fluorescence microscopy resides in estimating the axial position of particles with sub-resolution precision. Due to the complexity of the diffraction patterns generated by such particles, the standard fittin ...

We present a new fast active contour for images in 3D microscopy. We introduce a fully parametric design that relies on exponential B-spline bases and allows us to impose a sphere-like topology. The proposed 3D snake can approximate blob-like objects with ...

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 ...

We introduce a three-dimensional (3-D) parametric active contour algorithm for the shape estimation of DNA molecules from stereo cryo-electron micrographs. We estimate the shape by matching the projections of a 3-D global shape model with the micrographs; ...

Michaël Unser

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Full Flow/Motion-Field Recovery from Pulsed-Wave Ultrasound Doppler Data

Convergence analysis of the discretization of continuous-domain inverse problems

Unwarping of Unidirectionally Distorted EPI Images

Controlled Exchange of Chromosomal Arms Reveals Principles Driving Telomere Interactions in Yeast

Spline-Based Deforming Ellipsoids for Interactive 3D Bioimage Segmentation

Optimal-Transport-Based Metric for SMLM

Joint Texture and Topography Estimation for Extended Depth of Field in Brightfield Microscopy

The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression

Fresnelets—A New Wavelet Basis for Digital Holography

Phaseless Diffraction Tomography With Regularized Beam Propagation

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

Multiframe SURE-LET denoising of timelapse fluorescence microscopy images

Generalized Sampling: A Variational Approach

Imaging cellular ultrastructures using expansion microscopy (U-ExM)

Interior Tomography Using 1D Generalized Total Variation. Part II: Multiscale Implementation

Image Processing Education

A Maximum-Likelihood Formalism for Sub-Resolution Axial Localization of Fluorescent Nanoparticles

Fast Parametric Snakes For 3D Microscopy

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

3-D Shape Estimation of DNA Molecules from Stereo Cryo-Electron Micro-Graphs Using a Projection-Steerable Snake