Publications by Michaël Unser

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Background—Objective, quantitative, segmental noninvasive/bedside measurement of cardiac motion is highly desirable in cardiovascular medicine, but current technology suffers from significant drawbacks, such as subjectivity of conventional echocardiographic reading, angle dependence of tissue Doppler measurements, radiation exposure by computer tomography, and infrastructure requirements in MRI. We hypothesized that computer vision technology could represent a powerful new paradigm for quantification in ech

In this paper, we provide a Banach-space formulation of supervised learning with generalized total-variation (gTV) regularization. We identify the class of kernel functions that are admissible in this framework. Then, we propose a variation of supervised l ...

This paper presents an algorithm based on a continuous framework for a posteriori angular and translational assignment in three-dimensional electron microscopy (3DEM) of single particles. Our algorithm can be used advantageously to refine the assignment of ...

Ruttimann et al. have proposed to use the wavelet transform for the detection and localization of activation patterns in functional magnetic resonance imaging (fMRI). Their main idea was to apply a statistical test in the wavelet domain to detect the coefficients that are significantly different from zero. Here, we improve the original method in the case of non-stationary Gaussian noise by replacing the original z-test by a t-test that takes into account the variability of each wavelet coefficient separatel

In supervised learning, the regularization path is sometimes used as a convenient theoretical proxy for the optimization path of gradient descent initialized from zero. In this paper, we study a modification of the regularization path for infinite-width 2- ...

We present a general Fourier-based method that provides an accurate prediction of the approximation error as a function of the sampling step T. Our formalism applies to an extended class of convolution-based signal approximation techniques, which includes interpolation, generalized sampling with prefiltering, and the projectors encountered in wavelet theory. We claim that we can predict the

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-approximation error, by integrating the spectrum of the function to approximate—not necessarily bandlimi

We propose a construction of new wavelet-like bases that are well suited for the reconstruction and processing of optically generated Fresnel holograms recorded on CCD-arrays. The starting point is a wavelet basis of

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to which we apply a unitary Fresnel transform. The transformed basis functions are shift-invariant on a level-by-level basis but their multiresolution properties are governed by the special form that the dilation operator takes in the Fresnel domain. We derive a Heisenberg-like unc

We present a new family of active surfaces for the semiautomatic segmentation of volumetric objects in 3D biomedical images. We represent our deformable model by a subdivision surface encoded by a small set of control points and generated through a geometr ...

Splines, which were invented by Schoenberg more than fifty years ago, constitute an elegant framework for dealing with interpolation and discretization problems. They are widely used in computer-aided design and computer graphics, but have been neglected in medical imaging applications, mostly as a consequence of what one may call the "bad press" phenomenon. Thanks to some recent research efforts in signal processing and wavelet-related techniques, the virtues of splines have been revived in our community.

In this paper, an approach is introduced based on differential operators to construct wavelet-like basis functions. Given a differential operator L with rational transfer function, elementary building blocks are obtained that are shifted replicates of the ...

In this work we propose a variational reconstruction algorithm for enhancement and denoising of flow fields that is reminiscent of total-variation (TV) regularization used in image processing, but which also takes into account physical properties of flow s ...

The connection between derivative operators and wavelets is well known. Here we generalize the concept by constructing multiresolution approximations and wavelet basis functions that act like Fourier multiplier operators. This construction follows from a s ...

We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising) and the signal in-between (interpolation problem). By relying on tools fro ...

Localization microscopy achieves nanoscale spatial resolution by iterative localization of sparsely activated molecules, which generally leads to a long acquisition time. By implementing advanced algorithms to treat overlapping point spread functions (PSFs ...

We introduce a general distributional framework that results in a unifying description and characterization of a rich variety of continuous-time stochastic processes. The cornerstone of our approach is an innovation model that is driven by some generalized ...

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 ...

In recent years, compressed sensing techniques have been applied to the reconstruction of parallel magnetic resonance (MR) images. Particularly for 3D MR signal, it is crucial to acquire fewer samples to reduce the distortions caused by long-time acquisiti ...

We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions-the B-spline factorization theorem. In particular, starting from well-localized sc ...

We present new quantitative results for the characterization of the

L _{ 2 }

-error of wavelet-like expansions as a function of the scale a. This yields an extension as well as a simplification of the asymptotic error formulas that have been published previously. We use our bound determinations to compare the approximation power of various families of wavelet transforms. We present explicit formulas for the leading asymptotic constant for both splines and Daubechies wavelets. For a specified approximati

The characteristic functional is the infinite-dimensional generalization of the Fourier transform for measures on function spaces. It characterizes the statistical law of the associated stochastic process in the same way as a characteristic function specif ...

Michaël Unser

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Multiscale Motion Mapping—A Novel Computer Vision Technique for Quantitative, Objective Echocardiographic Motion Measurement Independent of Doppler: First Clinical Description and Validation

Multikernel Regression with Sparsity Constraint

Spline-Based Image-to-Volume Registration for Three-Dimensional Electron Microscopy

Optimizing Wavelets for the Analysis of fMRI Data

On the Effect of Initialization: The Scaling Path of 2-Layer Neural Networks

Quantitative Fourier Analysis of Approximation Techniques: Part I—Interpolators and Projectors

Fresnelets: New Multiresolution Wavelet Bases for Digital Holography

Active Subdivision Surfaces for the Semiautomatic Segmentation of Biomedical Volumes

Splines: A Perfect Fit for Medical Imaging

From Differential Equations to the Construction of New Wavelet-Like Bases

Variational Enhancement And Denoising Of Flow Field Images

Operator-Like Wavelet Bases of $ L _{ 2 } $ $ (\mathbb{R} ^{ d } $ )

Bayesian Estimation for Continuous-Time Sparse Stochastic Processes

3D high-density localization microscopy using hybrid astigmatic/biplane imaging and sparse image reconstruction

A Unified Formulation of Gaussian Versus Sparse Stochastic Processes-Part I: Continuous-Domain Theory

Wavelet Shrinkage With Consistent Cycle Spinning Generalizes Total Variation Denoising

3D Bpconvnet To Reconstruct Parallel Mri

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

Comparison of Wavelets from the Point of View of Their Approximation Error

On the Continuity of Characteristic Functionals and Sparse Stochastic Modeling