Publications by Michaël Unser

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Cardinal Hermite exponential spline functions are a generalization of the classical cardinal Hermite polynomial splines. In this work we consider the 4-dimensional space

ε _{ 4 }

= {1, x,

e ^{ \alpha x }

e ^{ -\alpha x }

} with α ∈ $ ℝ ^{ + } ...

Reservoir Computing is a class of Recurrent Neural Networks with internal weights fixed at random. Stability relates to the sensitivity of the network state to perturbations. It is an important property in Reservoir Computing as it directly impacts perform ...

Most modern imaging systems incorporate a computational pipeline to infer the image of interest from acquired measurements. The Bayesian approach to solve such ill-posed inverse problems involves the characterization of the posterior distribution of the im ...

Super-resolution localization microscopy relies on sparse activation of photo-switchable probes. Such activation, however, introduces limited temporal resolution. High-density imaging overcomes this limitation by allowing several neighboring probes to be a ...

We develop a variational algorithm for reconstructing phase objects from a series of bright field micrographs. Our mathematical model is based on the transport-of-intensity equation (TIE), which links the phase of a complex field to the axial derivative of ...

Many recent algorithms for sparse signal recovery can be interpreted as maximum-a-posteriori (MAP) estimators relying on some specific priors. From this Bayesian perspective, state-of-the-art methods based on discrete-gradient regularizers, such as total-v ...

We present an iterative deconvolution algorithm that minimizes a functional with a non-quadratic wavelet-domain regularization term. Our approach is to introduce subband-dependent parameters into the bound optimization framework of Daubechies et al.; it is sufficiently general to cover arbitrary choices of wavelet bases (non-orthonormal or redundant). The resulting procedure alternates between the following two steps:

We introduce a new primal-dual reconstruction algorithm for fluorescence and bioluminescence tomography. As often in optical tomography, image reconstruction is performed by optimizing a multi-term convex cost function. Current reconstruction methods emplo ...

ICIP'05 Best Student Paper Award We investigate the use of quasi-interpolating approximation schemes, to construct an estimate of an unknown function from its given discrete samples. We show theoretically and with practical experiments that such methods pe ...

We present a new method for region of interest (ROI) reconstruction from high-resolution, nontruncated data in parallel-ray X-ray computed tomography (CT). Many of the approaches to ROI CT reconstruction in the literature rely on a costly forward projectio ...

Imaging systems can be designed using examples and methods similar to the techniques used in deep learning. We describe experimental results demonstrating optical tomography based on the learning approach. ...

Optoacoustic (OA) imaging combined with reversibly photoswitchable proteins has emerged as a promising technology for the high-sensitivity and multiplexed imaging of cells in live tissues in preclinical research. Through carefully designed illumination sch ...

We provide an amplitude-phase representation of the dual-tree complex wavelet transform by extending the fixed quadrature relationship of the dual-tree wavelets to arbitrary phase-shifts using the fractional Hilbert transform. (fHT). The fHT is a generaliz ...

Many practical applications require the reconstruction of images from irregularly sampled data. The spline formalism offers an attractive framework for solving this problem; the currently available methods, however, are hard to deploy for large-scale inter ...

Purpose: In the context of fluorescence diffuse optical tomography, determining the optimal way to exploit the time-resolved information has been receiving much attention and different features of the time-resolved signals have been introduced. In this art ...

The tracking of cell populations in time-lapse microscopy images enables high-throughput spatiotemporal measurements of cell dynamics. In this paper, we present a new algorithm to simultaneously track many cells in crowded areas. The algorithm runs in real ...

The steerable wavelet transform is a redundant image representation with the remarkable property that its basis functions can be adaptively rotated to a desired orientation. This makes the transform well-suited to the design of wavelet-based algorithms app ...

A crucial component of steerable wavelets is the radial profile of the generating function in the frequency domain. In this paper, we present an infinite-dimensional optimization scheme that helps us find the optimal profile for a given criterion over the ...

We establish a link between classical osculatory interpolation and modern convolution-based interpolation and use it to show that two well-known cubic convolution schemes are formally equivalent to two osculatory interpolation schemes proposed in the actuarial literature about a century ago. We also discuss computational differences and give examples of other cubic interpolation schemes not previously studied in signal and image processing.

We present some issues that arise when a geometric transformation is performed on an image or a volume. In particular, we illustrate the well-known problems of blocking, blurring, aliasing and ringing. Although the solution to these problems is trivial in an analog (optical) image processing system, their solution in a discrete (numeric) context is much more difficult. The modern trend of biomedical image processing is to fight these artifacts by using more sophisticated models that emphasize the quality of

Michaël Unser

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Cardinal Hermite Exponential Splines: Theoretical Insights and Applications to Active Contours

Asymptotic Stability in Reservoir Computing

Bayesian Inversion for Nonlinear Imaging Models Using Deep Generative Priors

Continuous Localization Using Sparsity Constraints for High-Density Super-Resolution Microscopy

Digital Phase Reconstruction via Iterative Solutions of Transport-of-Intensity Equation

Mmse Denoising Of Sparse Levy Processes Via Message Passing

A fast iterative thresholding algorithm for wavelet-regularized deconvolution

A Primal-Dual Reconstruction Algorithm For Fluorescence And Bioluminescence Tomography

Beyond Interpolation: Optimal Reconstruction by Quasi-Interpolation

Region Of Interest X-Ray Computed Tomography Via Corrected Back Projection

Learning from Examples in Optical Imaging

Model-based temporal unmixing towards quantitative photo-switching optoacoustic tomography

The Fractional Hilbert Transform And Dual-Tree Gabor-Like Wavelet Analysis

Reconstruction of Large, Irregularly Sampled Multidimensional Images. A Tensor-Based Approach

A Time-Domain Wavelet-Based Approach for Fluorescence Diffuse Optical Tomography

Multi-Target Tracking Of Packed Yeast Cells

Benefits of consistency in image denoising with steerable wavelets

Maximally Localized Radial Profiles for Tight Steerable Wavelet Frames

A Note on Cubic Convolution Interpolation

Geometric Aspects in 3D Biomedical Image Processing