Publications by Michaël Unser

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We describe various methods to process the data collected with a digital confocal microscope (DCM) in order to get more information than what we could get from a conventional confocal system. Different metrics can be extracted from the data collected with ...

We propose an algorithm for the 3-D reconstruction of DNA filaments from a pair of stereo cryo-electron micrographs. The underlying principle is to specify a 3-D model of a filament—described as a spline curve—and to fit it to the 2-D data using a snake-like algorithm. To drive the snake, we constructed a ridge-enhancing vector field for each of the images based on the maximum output of a bank of rotating matched filters. The magnitude of the field gives a confidence measure for the presence of a filament a

Reconstruction algorithms for fluorescence tomography have to address two crucial issues : 1) the ill-posedness of the reconstruction problem, 2) the large scale of numerical problems arising from imaging of 3-D samples. Our contribution is the design and ...

B-splines are attractive basis functions for the continuous-domain representation of biomedical images and volumes. In this paper, we prove that the extended family of box splines are closed under the Radon transform and derive explicit formulae for their ...

While structured-illumination microscopy (SIM) is inherently a three-dimensional (3-D) technique, many biological questions can be addressed from the acquisition of a single focal plane with high lateral resolution. Unfortunately, the single-slice reconstr ...

In this work, we propose a continuous-domain stochastic model that can be applied to image data. This model is autoregressive, and accounts for Gaussian-type as well as for non-Gaussian-type innovations. In order to estimate the corresponding parameters fr ...

We introduce a 3-D parametric active contour algorithm for the shape estimation of DNA molecules from stereo cryo-electron micrographs. We consider a 3-D filament (consisting of a B-spline skeleton and a specified radial profile) and match its projections with the micrographs using an optimization algorithm. To accelerate the evaluation of the projections, we approximate the global model locally by an elongated blob-like template that is designed to be projection-steerable. This means that the 2-D projectio

We present a novel formulation for B-spline snakes that can be used as a tool for fast and intuitive contour outlining. The theory is implemented in a platform independent JAVA interface, which allows real time computation of the snake curve. In this paper, our main focus is on two points. First, we propose a novel B-spline snake formulation, where the intrinsic scale of the spline model is adjusted a priori. It leads to a reduction of the number of parameters to be optimized and eliminates the need for int

Localization microscopy such as STORM/PALM achieves the super-resolution by sparsely activating photo-switchable probes. However, to make the activation sparse enough to obtain reconstruction images using conventional algorithms, only small set of probes n ...

Statistical Parametric Mapping (SPM) is a widely deployed tool for detecting and analyzing brain activity from fMRI data. One of SPM's main features is smoothing the data by a Gaussian filter to increase the SNR. The subsequent statistical inference is based on the continuous Gaussian random field theory. Since the remaining spatial resolution has deteriorated due to smoothing, SPM introduces the concept of “resels” (resolution elements) or spatial information-containing cells. The number of resels turns ou

We propose a novel multiresolution-multigrid based signal reconstruction method from arbitrarily spaced samples. The signal is reconstructed on a uniform grid using B-splines basis functions. The computation of spline weights is formulated as a variational problem. Specifically, we minimize a cost that is a weighted sum of two terms: (i) the sum of squared errors at the specified points; (ii) a quadratic functional that penalizes the lack of smoothness. The problem is equivalent to solving a very large syst

Phase retrieval consists in the recovery of a complex-valued signal from intensity-only measurements. As it pervades a broad variety of applications, many researchers have striven to develop phase-retrieval algorithms. Classical approaches involve techniqu ...

The theory of sparse stochastic processes offers a broad class of statistical models to study signals, far beyond the more classical class of Gaussian processes. In this framework, signals are represented as realizations of random processes that are soluti ...

We present a method for the identification and classification of local symmetries in biological images. We aim at obtaining a precise estimate of symmetric junctions in a scale and rotation invariant way. The proposed method is template-free, which allows ...

We consider using spline interpolation to improve the standard filtered back-projection (FBP) tomographic reconstruction algorithm. In particular, we propose to link the design of the filtering operator with the interpolation model that is applied to the sinogram. The key idea is to combine the ramp filtering and the spline fitting process into a single filtering operation. We consider three different approaches. In the first, we simply adapt the standard FBP for spline interpolation. In the second approach

The efficient realization of linear space-variant (non-convolution) filters is a challenging computational problem in image processing. In this paper, we demonstrate that it is possible to filter an image with a Gaussian-like elliptic window of varying siz ...

Modern deconvolution algorithms are often specified as minimization problems involving a non-quadratic regularization functional. When the latter is a wavelet-domain l(1)-norm that favors sparse solutions, the problem can be solved by a simple iterative sh ...

We propose an amplitude-phase representation of the dual-tree complex wavelet transform (DT-ℂWT) which provides an intuitive interpretation of the associated complex wavelet coefficients. The representation, in particular, is based on the shifting action o ...

We address the problem of exact signal recovery in frequency domain optical coherence tomography (FDOCT) systems. Our technique relies on the fact that, in a spectral interferometry setup, the intensity of the total signal reflected from the object is smal ...

In the field of image segmentation, most level-set-based active-contour approaches take advantage of a discrete representation of the associated implicit function. We present in this paper a different formulation where the implicit function is modeled as a ...

Michaël Unser

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Multiple contrast metrics from the measurements of a digital confocal microscope

3-D Reconstruction of DNA Filaments from Stereo Cryo-Electron Micrographs

An Efficient Numerical Method for General

A Box Spline Calculus for the Discretization of Computed Tomography Reconstruction Problems

Computational Super-Sectioning for Single-Slice Structured-Illumination Microscopy

Linear Interpolation Of Biomedical Images Using A Data-Adaptive Kernel

Shape Estimation of 3-D DNA Molecules from Stereo Cryo-Electron Micro-Graphs

B-Spline Snakes and a JAVA Interface: An Intuitive Tool for General Contour Delineation

Fast Maximum Likelihood High-Density Low-SNR Super-Resolution Localization Microscopy

Wavelets Versus Resels in the Context of fMRI: Establishing the Link with SPM

Multigrid Image Reconstruction from Arbitrarily Spaced Samples

Phase Retrieval: From Computational Imaging to Machine Learning: A tutorial

Gaussian and sparse processes are limits of generalized Poisson processes

Wavelet-Based Identification and Classification of Local Symmetries in Microscopy Images

Filter Design for Filtered Back-Projection Guided by the Interpolation Model

Fast Space-Variant Elliptical Filtering Using Box Splines

Accelerated Wavelet-Regularized Deconvolution For 3-D Fluorescence Microcopy

Gabor Wavelet Analysis and the Fractional Hilbert Transform

Non-iterative exact signal recovery in frequency domain optical coherence tomography

Variational B-Spline Level-Set: A Linear Filtering Approach for Fast Deformable Model Evolution