Publications by Michaël Unser

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The Schizosaccharomyces pombe septation initiation network (SIN) regulates cytokinesis, and asymmetric association of SIN proteins with the mitotic spindle pole bodies (SPBs) is important for its regulation. Here, we have used semi-automated image analysis ...

We propose an image-based elastography method to measure the heterogeneous stiffness inside a cell and its nucleus. It uses a widely accessible setup consisting of plate compression imaged with fluorescence microscopy. Our framework recovers a spatial map ...

We introduce an Nth-order extension of the Riesz transform in d dimensions. We prove that this generalized transform has the following remarkable properties: shift-invariance, scale-invariance, inner-product preservation, and steerability. The pleasing con ...

Scanning transmission X-ray microscopy (STXM) produces images in which each pixel value is related to the measured attenuation of an X-ray beam. In practice, the location of the illuminated region does not exactly match the desired uniform pixel grid. This ...

In this paper we propose a method based on (2, 1)-mixed-norm penalization for incorporating a structural prior in FDOT image reconstruction. The effect of (2, 1)-mixed-norm penalization is twofold: first, a sparsifying effect which isolates few anatomical ...

Due to the limited depth of field of brightfield microscopes, it is usually impossible to image thick specimens entirely in focus. By optically sectioning the specimen, the in-focus information at the specimen's surface can be acquired over a range of imag ...

We introduce local weighted geometric moments that are computed from an image within a sliding window at multiple scales. When the window function satisfies a two-scale relation, we prove that lower order moments can be computed efficiently at dyadic scales by using a multiresolution wavelet-like algorithm. We show that B-splines are well-suited window functions because, in addition to being refinable, they are positive, symmetric, separable, and very nearly isotropic (Gaussian shape). We present three appl

The purpose of this note is to highlight some of the unique properties of spline wavelets. These wavelets can be classified in four categories: othogonal (Battle-Lemarié), semi-orthogonal (e.g., B-spline), shift-orthogonal, and biorthogonal (Cohen-Daubechies-Feauveau). Unlike most other wavelet bases, splines have explicit formulae in both the time and frequency domain, which greatly facilitates their manipulation. They allow for a progressive transition between the two extreme cases of a multiresolution: H

We consider the problem of optimizing the parameters of a given denoising algorithm for restoration of a signal corrupted by white Gaussian noise. To achieve this, we propose to minimize Stein's unbiased risk estimate (SURE) which provides a means of asses ...

We propose an efficient orthonormal wavelet-domain video denoising algorithm based on an appropriate integration of motion compensation into an adapted version of our recently devised Stein's unbiased risk estimator-linear expansion of thresholds (SURE-LET ...

We address the task of rendering by ray tracing the isosurface of a high-quality continuous spline model of volumetric discrete and regular data. By expressing the spline model as a sum of nonnegative B-splines, we are able to confine the potential location of the isosurface within a thin binary shell. We then show how to use the space-embedding property of splines to further shrink this shell to essentially a single-voxel width. We also propose a new illumination model that highlights the outline of the re

We present a new method for reconstructing digitally recorded off-axis Fresnel holograms. Currently-used reconstruction methods are based on the simulation and propagation of a reference wave that is diffracted by the hologram. This procedure introduces a twin-image and a zero-order term which are inherent to the diffraction phenomenon. These terms perturb the reconstruction and limit the field of view. Our new approach splits the reconstruction process into two parts. First, we recover the amplitude and th

One of the main factors that affect the accuracy of intensity-based registration of two-dimensional (2D) X-ray fluoroscopy to three-dimensional (3D) CT data is the similarity measure, which is a criterion function that is used in the registration procedure ...

Mycobacterium tuberculosis (Mtb) defends itself against host immunity and chemotherapy at several levels, including the repair or degradation of irreversibly oxidized proteins (IOPs). To investigate how Mtb deals with IOPs that can neither be repaired nor ...

To understand neural circuits that control limbs, one must measure their activity during behavior. Until now this goal has been challenging, because limb premotor and motor circuits have been largely inaccessible for large-scale recordings in intact, movin ...

Consider a random process s that is a solution of the stochastic differential equation Ls = w with L a homogeneous operator and w a multidimensional Levy white noise. In this paper, we study the asymptotic effect of zooming in or zooming out of the process ...

Many experimental paradigms in biology aim at studying the response to coordinated stimuli. In dynamic imaging experiments, the observed data is often not straightforward to interpret and not directly measurable in a quantitative fashion. Consequently, the ...

We address the task of rendering by ray tracing the isosurface of a high-quality continuous model of volumetric discrete and regular data. Based on first principles, we identify the quadratic B-spline as the best model for our purpose. The nonnegativity of this basis function allows us to confine the potential location of the isosurface within a binary shell. We then show how to use the space-embedding property of splines to further shrink this shell to essentially a single voxel width. Not all rays traced

We characterize the solution of a broad class of convex optimization problems that address the reconstruction of a function from a finite number of linear measurements. The underlying hypothesis is that the solution is decomposable as a finite sum of compo ...

We formulate an optimization problem to estimate probability densities in the context of multidimensional problems that are sampled with uneven probability. It considers detector sensitivity as an heterogeneous density and takes advantage of the computatio ...

Michaël Unser

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Analysis of S. pombe SIN protein association to the SPB reveals two genetically separable states of the SIN

PROBING INTRACELLULAR ELASTICITY WITH MINIMAL-HESSIAN REGISTRATION

Higher-Order Riesz Transforms And Steerable Wavelet Frames

Hessian Splines For Scanning Transmission X-Ray Microscopy

Sparsity-Driven Reconstruction for FDOT With Anatomical Priors

Model-Based 2.5-D Deconvolution for Extended Depth of Field in Brightfield Microscopy

Multiresolution Moment Filters: Theory and Applications

Ten Good Reasons for Using Spline Wavelets

Monte-Carlo SURE: A Black-Box Optimization of Regularization Parameters for General Denoising Algorithms

SURE-LET for Orthonormal Wavelet-Domain Video Denoising

High-Quality Isosurface Rendering with Exact Gradient

A Novel Non-Diffractive Reconstruction Method for Digital Holographic Microscopy

Point Similarity Measures Based on MRF Modeling of Difference Images for Spline-Based 2D-3D Rigid Registration of x-Ray Fluoroscopy to CT Images

Stressed Mycobacteria Use the Chaperone ClpB to Sequester Irreversibly Oxidized Proteins Asymmetrically Within and Between Cells

Imaging neural activity in the ventral nerve cord of behaving adult Drosophila

Scaling Limits of Solutions of Linear Stochastic Differential Equations Driven by Levy White Noises

Wavelet-Based Detection of Stimulus Responses in Time-Lapse Microscopy

Precision Isosurface Rendering of 3-D Image Data

Convex optimization in sums of Banach spaces

Sensitivity-Aware Density Estimation in Multiple Dimensions