Publications de Michaël Unser

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In this paper, we characterize the class of extremal points of the unit ball of the Hessian-Schatten total variation (HTV) functional. The underlying motivation for our work stems from a general representer theorem that characterizes the solution set of re ...

The Poisson summation formula (PSF), which relates the sampling of an analog signal with the periodization of its Fourier transform, plays a key role in the classical sampling theory. In its current forms, the formula is only applicable to a limited class ...

We present here an explicit time-domain representation of any compactly supported dyadic scaling function as a sum of harmonic splines. The leading term in the decomposition corresponds to the fractional splines, a recent, continuous-order generalization of the polynomial splines.

We propose here a new pointwise wavelet thresholding function that incorporates inter-scale dependencies. This non-linear function depends on a set of four linear parameters per subband which are set by minimizing Stein's unbiased MSE estimate (SURE). Our ...

Method of interpolating digital samples (fN, fn) using interpolation functions ( psi , psi (x-x0)) that are shifted by an arbitrary shift value (x0) relative to said samples (fN, fn). It will be shown that there is a non-zero and non-trivial optimal value for this shift value (x0) for which the approximation error is minimized.

Recently, we proposed a noniterative cepstral technique for exact signal recovery in frequency-domain optical-coherence tomography. In this paper, we address the influence of measurement noise on the performance of the method. We derive analytical expressi ...

We propose a novel algorithm for denoising Poisson-corrupted images, that performs a signal-adaptive thresholding of the undecimated Haar wavelet coefficients. A Poisson's unbiased MSE estimate is devised and adapted to arbitrary transform-domain pointwise ...

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 ...

This paper deals with the problem of time-resolved fluorescence diffuse optical tomography. We propose a new reconstruction scheme based on a multi-resolution approximation of the time-resolved signals. The underlying basis functions are exponential B-spli ...

State-of-the-art approaches to detecting ridge-like structures in images rely on filters designed to respond to locally linear intensity features. While these approaches may be optimal for ridges whose appearance is close to being ideal, their performance degrades quickly in the presence of structured noise that corrupts the image signal, potentially to the point where it truly does not conform to the ideal model anymore. In this paper, we address this issue by introducing a learning framework that relies o

We propose to optimize the activation functions of a deep neural network by adding a corresponding functional regularization to the cost function. We justify the use of a second-order total-variation criterion. This allows us to derive a general represente ...

We develop a fast algorithm for segmenting 3D images from linear measurements based on the Potts model (or piecewise constant Mumford-Shah model). To that end, we first derive suitable space discretizations of the 3D Potts model, which are capable of deali ...

We introduce a family of real and complex wavelet bases of

L _{ 2 }

(\mathbb{R} ^{ 2 }

) that are directly linked to the Laplace and Riesz operators. The crucial point is that the family is closed with respect to the Riesz transform which maps a re ...

Mutual information is a widely used similarity measure for aligning multimodal medical images. At its core it relies on the computation of a discrete joint histogram, which itself requires image samples for its estimation. In this paper we study the influe ...

Single-particle cryo-electron microscopy (cryo-EM) reconstructs the three-dimensional (3D) structure of bio-molecules from a large set of 2D projection images with random and unknown orientations. A crucial step in the single-particle cryo-EM pipeline is 3 ...

We present an algorithm for nonlinear multidimensional registration. The correspondence function is represented in a spline space, as well as the volumes being registered. We also use the cubic splines to interpolate the volumetric data to be registered. We use a multiresolution strategy, which gives us robustness and additional speedup. We analyze the computational complexity of the algorithm and its performance using different multidimensional optimization methods. Finally, we present an application of th

We use a comprehensive set of non-redundant orthogonal wavelet transforms and apply a denoising method called SUREshrink in each individual wavelet subband to denoise images corrupted by additive Gaussian white noise. We show that, for various images and a ...

We address the problem of exact complex-wave reconstruction in digital holography. We show that, by confining the object-wave modulation to one quadrant of the frequency domain, and by maintaining a reference-wave intensity higher than that of the object, ...

Following on from the emerging importance of the pancreas circadian clock on islet function and the development of type 2 diabetes in rodent models, we aimed to examine circadian gene expression in human islets. The oscillator properties were assessed in i ...

We extend the classical interpolation method to generalized interpolation. This extension is done by replacing the interpolating function by a non-interpolating function that is applied to prefiltered data, in order to preserve the interpolation condition. We show, both theoretically and practically, that this approach performs much better than classical methods, for the same computational cost.

Michaël Unser

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Linear inverse problems with Hessian-Schatten total variation

Generalized Poisson Summation Formula for Tempered Distributions

Harmonic Spline Series Representation of Scaling Functions

SURE-Based Wavelet Thresholding Integrating Inter-Scale Dependencies

Interpolation method and apparatus

Performance analysis of the cepstral technique for frequency-domain optical-coherence tomography

Undecimated Haar Thresholding For Poisson Intensity Estimation

One-Bit Measurements With Adaptive Thresholds

Time Resolved Fluorescence Diffuse Optical Tomography Using Multi-Resolution Exponential B-Splines

Rotational Features Extraction for Ridge Detection

A Representer Theorem for Deep Neural Networks

Fast Segmentation from Blurred Data in 3D Fluorescence Microscopy

The Monogenic Riesz-Laplace Wavelet Transform

Halton Sampling for Image Registration Based on Mutual Information

Joint Angular Refinement and Reconstruction for Single-Particle Cryo-EM

Multidimensional Elastic Registration of Images Using Splines

Which Wavelet Bases Are the Best for Image Denoising?

Exact Complex-Wave Reconstruction in Digital Holography

Autonomous and self-sustained circadian oscillators displayed in human islet cells

Generalized Interpolation: Higher Quality at no Additional Cost