Publications by Michaël Unser

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

This work puts forward an extended definition of vector fractional Brownian motion (fBm) using a distribution theoretic formulation in the spirit of Gel′fand and Vilenkin's stochastic analysis. We introduce random vector fields that share the statistical i ...

We propose a new optimizer in the context of multimodal image registration. The optimized criterion is the mutual in formation between the images to align. This criterion requires that their joint histogram be available. For its computation, we introduce differentiable and separable Parzen windows that satisfy the partition of unity. Along with a continuous model of the images based on splines, this allows us to derive exact and tractable expressions for the gradient and the Hessian of the criterion. Then,

The measurement of brain activity in a noninvasive way is an essential element in modern neurosciences. Modalities such as electroencephalography (EEG) and magnetoencephalography (MEG) recently gained interest, but two classical techniques remain predomina ...

Magnetic resonance spectroscopy imaging (MRSI) is a promising and developing tool in medical imaging. Because of various difficulties imposed by the imperfections of the scanner and the reconstruction algorithms, its applicability in clinical practice is r ...

The usual explanation of the efficacy of wavelet-based methods hinges on the sparsity of many real-world objects in the wavelet domain. Yet, standard wavelet-shrinkage techniques for sparse reconstruction are not competitive in practice, one reason being t ...

The “Marr wavelet pyramid” is a wavelet decomposition that implements a multiscale version of the complex gradient-Laplace operator. It is closely linked to a multiresolution analysis of

L _{ 2 }

(\mathbb{R} ^{ 2 }

) and it has a fast filterbank im ...

In this note we introduce a vector generalization of fractional Brownian motion. Our definition takes into account directional properties of vector fields-such as divergence, rotational behaviour, and interactions with coordinate transformations-that have ...

The LeGall 5⁄3 and Daubechies 9⁄7 filters have risen to special prominence because they were selected for inclusion in the JPEG2000 standard. Here, we determine their key mathematical features: Riesz bounds, order of approximation, and regularity (Hölder and Sobolev). We give approximation theoretic quantities such as the asymptotic constant for the

L ^{ 2 }

error and the angle between the analysis and synthesis spaces which characterizes the loss of performance with respect to an orthogonal projection.

We present an explicit formula for spline kernels; these are defined as the convolution of several B-splines of variable widths h and degrees n. The spline kernels are useful for continuous signal processing algorithms that involve B-spline inner-products or the convolution of several spline basis functions. We apply our results for the derivation of spline-based algorithms for two classes of problems. The first is the resizing of images with arbitrary scaling factors. The second problem is the computation

We propose an algorithm for aligning a preoperative computed tomography (CT) volume and intraoperative C-arm images, with applications in computer-assisted spinal surgery. Our three-dimensional (3D)/two-dimensional (2D) registration algorithm is based on splines and is tuned to a multiresolution strategy. Its goal is to establish the mutual relations of locations in the real-world scene to locations in the 3D CT and inthe 2D C-arm images. The principle of the solution is to simulate a series of C-arm images

Wavelet-domain l(1)-regularization is a promising approach to deconvolution. The corresponding variational problem can be solved using a "thresholded Landweber" (TL) algorithm. While this iterative procedure is simple to implement, it is known to converge ...

We present an affine-invariant non-stationary subdivision scheme for the recursive refinement of any triangular mesh that is regular or has extraordinary vertices of valence 4. In particular, when applied to an arbitrary convex octahedron, it produces a $ ...

In this article we propose a cardiac motion estimation technique that uses non-rigid registration to compute the dense cardiac displacement field from 2D ultrasound sequences. Our method employs a semi-local deformation model which provides controlled smoothness. We apply a multiresolution optimization strategy for better speed and robustness. To further improve the accuracy, the sequence is registered in both forward and backward directions. We calculate additional parameters from the displacement field, s

The Poisson summation formula (PSF) describes the equivalence between the sampling of an analog signal and the periodization of its frequency spectrum. In engineering textbooks, the PSF is usually stated formally without explicit conditions on the signal f ...

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 ...

We present a zero-order and twin image elimination algorithm for digital Fresnel holograms that were acquired in an off-axis geometry. These interference terms arise when the digital hologram is reconstructed and corrupt the result. Our algorithm is based on the Fresnelet transform, a wavelet-like transform that uses basis functions tailor-made for digital holography. We show that in the Fresnelet domain, the coefficients associated to the interference terms are separated both spatially and with respect to

Image processing is getting more and more important because of the widespread use of digital imaging devices, such as digital cameras or digital videos. While image processing is a very practical discipline, it is perceived as being rather theoretical. It ...

Thanks to recent advances in signal processing, the interest for fast ℓ1-regularized reconstruction algorithms in cryo-electron microscopy (cryo-EM) has intensified. The approaches based on the alternating-direction of multipliers method (ADMM) are particu ...

We have designed a series of computer sessions build around ImageJ (a public-domain software for image analysis), as a practical complement to a two-semester course in image processing. The students are challenged with simple practical imaging problems as they acquire hands-on practice by experimenting with image-processing operators. In the process, they also learn how to program standard image-processing algorithms in Java. This is made possible thanks to a programmer-friendly environment and a software i

A new method based on the Young-Laplace equation for measuring contact angles and surface tensions is presented. In this approach, a first-order perturbation technique helps to analytically solve the Young-Laplace equation according to photographic images ...

Michaël Unser

Chat with Graph Search

Fractional Brownian Vector Fields

An Efficient Mutual Information Optimizer for Multiresolution Image Registration

Surfing the Brain—An Overview of Wavelet-Based Techniques for fMRI Data Analysis

Improved MRSI with Field Inhomogeneity Compensation

The Sparsity of Cycle Spinning for Wavelet-Based Solutions of Linear Inverse Problems

The Marr Wavelet Pyramid and Multiscale Directional Image Analysis

Fractional Brownian Models For Vector Field Data

Mathematical Properties of the JPEG2000 Wavelet Filters

Spline kernels for continuous-space image processing

Multiresolution Spline-Based 3D/2D Registration of CT Volume and C-Arm Images for Computer-Assisted Surgery

A fast thresholded landweber algorithm for general wavelet bases: Application to 3D deconvolution microscopy

A Non-Stationary Subdivision Scheme for the Construction of Deformable Models with Sphere-Like Topology

Cardiac Motion Analysis from Ultrasound Sequences Using Non-Rigid Registration

Generalized Poisson Summation Formulas for Continuous Functions of Polynomial Growth

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

Non-Linear Fresnelet Approximation for Interference Term Suppression in Digital Holography

IP-LAB: A Tool to Teach Image Processing Programming in Java—Challenge in Swiss Federal Institute of Technology Lausanne

Inner-Loop-Free ADMM for Cryo-EM

Easy Java Programming for Teaching Image Processing

Low-Bond Axisymmetric Drop Shape Analysis for Surface Tension and Contact Angle Measurements of Sessile Drops