Publications by Michaël Unser

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Causal exponentials play a fundamental role in classical system theory. Starting from those elementary building blocks, we propose a complete and self-contained signal processing formulation of exponential splines defined on a uniform grid. We specify the ...

We study one-dimensional continuous-domain inverse problems with multiple generalized total-variation regularization, which involves the joint use of several regularization operators. Our starting point is a new representer theorem that states that such in ...

We present a new wavelet-based strategy for autonomous feature extraction and segmentation of cardiac structures in dynamic ultrasound images. Image sequences subjected to a multidimensional (2D plus time) wavelet transform yield a large number of individual subbands, each coding for partial structural and motion information of the ultrasound sequence. We exploited this fact to create an analysis strategy for autonomous analysis of cardiac ultrasound that builds on shape- and motion specific wavelet subband

The minimization of a data-fidelity term and an additive regularization functional gives rise to a powerful framework for supervised learning. In this paper, we present a unifying regularization functional that depends on an operator L\documentclass[12pt]{ ...

A convolution algebra is a topological vector space X that is closed under the convolution operation. It is said to be inverse-closed if each element of X whose spectrum is bounded away from zero has a convolution inverse that is also part of the algebra. ...

The monogenic signal is the natural 2-D counterpart of the 1-D analytic signal. We propose to transpose the concept to the wavelet domain by considering a complexified version of the Riesz transform which has the remarkable property of mapping a real-value ...

We present a multiscale reconstruction framework for single-particle analysis (SPA). The representation of three-dimensional (3D) objects with scaled basis functions permits the reconstruction of volumes at any desired scale in the real-space. This multisc ...

We present a statistical framework to benchmark the performance of reconstruction algorithms for linear inverse problems, in particular, neural-network-based methods that require large quantities of training data. We generate synthetic signals as realizati ...

Shannon's sampling theory and its variants provide effective solutions to the problem of reconstructing a signal from its samples in some “shift-invariant” space, which may or may not be bandlimited. In this paper, we present some further justification for ...

We introduce a general framework for the reconstruction of vector-valued functions from finite and possibly noisy data, acquired through a known measurement operator. The reconstruction is done by the minimization of a loss functional formed as the sum of a convex data fidelity functional and a total-variation-based regularizer involving a suitable matrix L of differential operators. Here, the total variation is a norm on the space of vector measures. These are split into two categories: inner, and outer no

In this paper, we perform the joint study of scale -invariant operators and self -similar processes of complex order. More precisely, we introduce general families of scale -invariant complex -order fractional -derivation and integration operators by const ...

Background: The yeast Schizosaccharomyces pombe is frequently used as a model for studying the cell cycle. The cells are rod-shaped and divide by medial fission. The process of cell division, or cytokinesis, is controlled by a network of signaling proteins ...

With the recent development of fluorescent probes and new high-resolution microscopes, biological imaging has entered a new era and is presently having a profound impact on the way research is being conducted in the life sciences. Biologists have come to d ...

Localisation microscopy often relies on detailed models of point‐spread functions. For applications such as deconvolution or PSF engineering, accurate models for light propagation in imaging systems with a high numerical aperture are required. Different models have been proposed based on 2D Fourier transforms or 1D Bessel integrals. The most precise ones combine a vectorial description of the electric field and accurate aberration models. However, it may be unclear which model to choose as there is no compr

We present a method for the exact computation of the moments of a region bounded by a curve represented by a scaling function or wavelet basis. Using Green's Theorem, we show that the computation of the area moments is equivalent to applying a suitable multidimensional filter on the coefficients of the curve and thereafter computing a scalar product. The multidimensional filter coefficients are precomputed exactly as the solution of a two-scale relation. To demonstrate the performance improvement of the new

The formulation of inverse problems in the continuum eliminates discretization errors and allows for the exact incorporation of priors. In this paper, we formulate a continuous-domain inverse problem over a search space of continuous and piecewise-linear f ...

The present invention discloses a method and an apparatus to compute a complex wavefield, referred to as the object wave o, by means of measuring the intensity signal resulting from the interference of the said object wave with a second wave termed the ref ...

Inverse problems with shot noise arise in many modern biomedical imaging applications. The main challenge is to obtain an estimate of the underlying specimen from measurements corrupted by Poisson noise. In this work, we propose an efficient framework for ...

Optical imaging is a powerful technique to map brain function in animals. In this study, we consider in vivo optical imaging of the murine olfactory bulb, using an intrinsic signal and a genetically expressed activity reporter fluorescent protein (synaptop ...

An interpolation model is a necessary ingredient of intensity-based registration methods. The properties of such a model depend entirely on its basis function, which has been traditionally characterized by features such as its order of approximation and it ...

Michaël Unser

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Cardinal Exponential Splines: Part I—Theory and Filtering Algorithms

Hybrid-Spline Dictionaries for Continuous-Domain Inverse Problems

Multidimensional, Multistage Wavelet Footprints: A New Tool for Image Segmentation and Feature Extraction in Medical Ultrasound

From Kernel Methods to Neural Networks: A Unifying Variational Formulation

Beyond Wiener's Lemma: Nuclear Convolution Algebras and the Inversion of Digital Filters

Multiresolution Monogenic Signal Analysis Using the Riesz-Laplace Wavelet Transform

Fast multiscale reconstruction for Cryo-EM

A Statistical Framework to Investigate the Optimality of Signal-Reconstruction Methods

Sampling in Practice: Is the Best Reconstruction Space Bandlimited?

Adaptive vector-valued splines for the resolution of inverse problems

Complex-order scale-invariant operators and self-similar processes

A 2D/3D image analysis system to track fluorescently labeled structures in rod-shaped cells: application to measure spindle pole asymmetry during mitosis

The Colored Revolution of Bioimaging

Revisiting PSF models: Unifying framework and high‐performance implementation

An Exact Method for Computing the Area Moments of Wavelet and Spline Curves

A Box-Spline Framework for Inverse Problems With Continuous-Domain Sparsity Constraints

A method and apparatus for enhanced spatial bandwidth wavefronts reconstructed from digital interferograms or holograms

3D Poisson Microscopy Deconvolution With Hessian Schatten-Norm Regularization

Wavelet-Based Statistical Analysis for Optical Imaging in Mouse Olfactory Bulb

Short basis functions for constant-variance interpolation