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Michaël Unser

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Publications associées (516)

A Dual Algorithm for $ L _{ 1 } $ -Regularized Reconstruction of Vector Fields

Michaël Unser, Pouya Dehghani Tafti, Emrah Bostan

Recent advances in vector-field imaging have brought to the forefront the need for efficient denoising and reconstruction algorithms that take the physical properties of vector fields into account and can be applied to large volumes of data. With these req ...

IEEE2012

Experimental investigation of collagen waviness and orientation in the arterial adventitia using confocal laser scanning microscopy

Nikolaos Stergiopoulos, Michaël Unser, Daniel Sage, Alessandra Griffa, Aristotelis Agianniotis, Jelle Tymen Christiaan Schrauwen

Mechanical properties of the adventitia are largely determined by the organization of collagen fibers. Measurements on the waviness and orientation of collagen, particularly at the zero-stress state, are necessary to relate the structural organization of c ...

Springer Verlag2012

Left-inverses of fractional Laplacian and sparse stochastic processes

Michaël Unser

The fractional Laplacian (-Delta)(gamma/2) commutes with the primary coordination transformations in the Euclidean space Rd: dilation, translation and rotation, and has tight link to splines, fractals and stable Levy processes. For 0 < gamma < d, its inver ...

Springer2012

Hessian-Based Norm Regularization for Image Restoration With Biomedical Applications

Michaël Unser, Aurélien Bourquard, Stamatios Lefkimmiatis

We present nonquadratic Hessian-based regularization methods that can be effectively used for image restoration problems in a variational framework. Motivated by the great success of the total-variation (TV) functional, we extend it to also include second- ...

IEEE2012

A Projected Gradient Algorithm for Image Restoration Under Hessian Matrix-Norm Regularization

Michaël Unser, Stamatios Lefkimmiatis

We have recently introduced a class of non-quadratic Hessian-based regularizers as a higher-order extension of the total variation (TV) functional. These regularizers retain some of the most favorable properties of TV while they can effectively deal with t ...

IEEE2012

Is Uniqueness Lost for Under-Sampled Continuous-Time Auto-Regressive Processes?

Michaël Unser, Hagay Kirshner, John Paul Ward

We consider the problem of sampling continuous-time auto-regressive processes on a uniform grid. We investigate whether a given sampled process originates from a single continuous-time model, and address this uniqueness problem by introducing an alternativ ...

IEEE Institute of Electrical and Electronics Engineers2012

Hessian-Based Regularization For 3-D Microscopy Image Restoration

Michaël Unser, Aurélien Bourquard, Stamatios Lefkimmiatis

We investigate a non quadratic regularizer that is based on the Hessian operator for dealing with the restoration of 3-D images in a variational framework. We show that the regularizer under study is a valid extension of the total-variation (TV) functional ...

Ieee2012

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

Michaël Unser, Masih Nilchian

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 ...

Institute of Electrical and Electronics Engineers2012

One-Bit Measurements With Adaptive Thresholds

Michaël Unser, Aurélien Bourquard, Ulugbek Kamilov, Arash Amini

We introduce a new method for adaptive one-bit quantization of linearmeasurements and propose an algorithm for the recovery of signals based on generalized approximate message passing (GAMP). Our method exploits the prior statistical information on the sig ...

IEEE Institute of Electrical and Electronics Engineers2012

Stochastic Models and Techniques for Sparse Signals

Michaël Unser, Azin Amini

Real-world data such as multimedia, biomedical, and telecommunication signals are formed of specific structures. However, these structures only determine some general properties of the data while the unknown or unpredictable parts are assumed to be random. ...

IEICE2012

Wavelet Shrinkage With Consistent Cycle Spinning Generalizes Total Variation Denoising

Michaël Unser, Ulugbek Kamilov, Emrah Bostan

We introduce a new wavelet-based method for the implementation of Total-Variation-type denoising. The data term is least-squares, while the regularization term is gradient-based. The particularity of our method is to exploit a link between the discrete gra ...

IEEE Institute of Electrical and Electronics Engineers2012

3D Steerable Wavelets in Practice

Michaël Unser

We introduce a systematic and practical design for steerable wavelet frames in 3D. Our steerable wavelets are obtained by applying a 3D version of the generalized Riesz transform to a primary isotropic wavelet frame. The novel transform is self-reversible ...

Institute of Electrical and Electronics Engineers2012

Bayesian Denoising Of Generalized Poisson Processes With Finite Rate Of Innovation

Michaël Unser, Ulugbek Kamilov, Arash Amini

We investigate the problem of the optimal reconstruction of a generalized Poisson process from its noisy samples. The process is known to have a finite rate of innovation since it is generated by a random stream of Diracs with a finite average number of im ...

Ieee2012

Differential Phase-Contrast X-Ray Computed Tomography: From Model Discretization To Image Reconstruction

Michaël Unser, Masih Nilchian

Our contribution in this paper is two fold. First, we propose a novel discretization of the forward model for differential phase-contrast imaging that uses B-spline basis functions. The approach yields a fast and accurate algorithm for implementing the for ...

Ieee2012

Generalized Total Variation Denoising Via Augmented Lagrangian Cycle Spinning With Haar Wavelets

Michaël Unser, Ulugbek Kamilov, Emrah Bostan

We consider the denoising of signals and images using regularized least-squares method. In particular, we propose a simple minimization algorithm for regularizers that are functions of the discrete gradient. By exploiting the connection of the discrete gra ...

Ieee2012

Local demodulation of holograms using the Riesz transform with application to microscopy

Christian Depeursinge, Michaël Unser, Nicolas Pavillon, Chandra Sekhar Seelamantula

We propose a Riesz transform approach to the demodulation of digital holograms. The Riesz transform is a higher-dimensional extension of the Hilbert transform and is steerable to a desired orientation. Accurate demodulation of the hologram requires a relia ...

Optical Society of America2012

Fast Parametric Snakes For 3D Microscopy

Michaël Unser, Ricard Delgado Gonzalo

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 ...

Ieee2012

Reconstruction Of Biomedical Images And Sparse Stochastic Modeling

Michaël Unser, Ulugbek Kamilov, Emrah Bostan

We propose a novel statistical formulation of the image-reconstruction problem from noisy linear measurements. We derive an extended family of MAP estimators based on the theory of continuous-domain sparse stochastic processes. We highlight the crucial rol ...

Ieee2012

Image Segmentation With Background Correction Using A Multiplicative Smoothing-Spline Model

Michaël Unser, Aurélien Bourquard, Ramtin Madani

This paper presents an image-segmentation method which compensates multiplicative distortions based on smooth regularity assumptions. In this work, we generalize the original Chan-Vese functional to handle a continuous multiplicative bias. In the derivatio ...

Ieee2012

Realistic Analytical Phantoms for Parallel Magnetic Resonance Imaging

Michaël Unser, Matthieu Guerquin-Kern

The quantitative validation of reconstruction algorithms requires reliable data. Rasterized simulations are popular but they are tainted by an aliasing component that impacts the assessment of the performance of reconstruction. We introduce analytical simu ...

Institute of Electrical and Electronics Engineers2012

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