Publications by Michaël Unser

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We define multi-scale moments that are estimated locally by analyzing the image through a sliding window at multiple scales. When the analysis window satisfies a two-scale relation, we prove that these moments can be computed very efficiently using a multiresolution wavelet-like algorithm. We also show that B-spline windows are best suited for this kind of analysis because, in addition to being refinable, they are positive, symmetric and very nearly isotropic. We present two applications of our method. The

Lensless quantitative phase imaging is of high interest for obtaining a large field of view (FOV), typically the size of the camera chip, to observe biological cell material with high contrast. It has the potential to be widely spread due to its inherent s ...

This paper introduces a new approach to orthonormal wavelet image denoising. Instead of postulating a statistical model for the wavelet coefficients, we directly parametrize the denoising process as a sum of elementary nonlinear processes with unknown weig ...

We study a variant of the interpolation problem where the continuously defined solution is regularized by minimizing the L p -norm of its second-order derivative. For this continuous-domain problem, we propose an exact discretization scheme that restricts ...

We present a semiautomated software solution to the problem of extending the lateral field of view of a classical microscope. The initial requirements are a set of overlapping images, along with their user-provided coarse mosaic. Our solution then refines ...

Optical diffraction tomography (ODT) allows one to quantitatively measure the distribution of the refractive index of the sample. It relies on the resolution of an inverse scattering problem. Due to the limited range of views as well as optical aberrations ...

We address the problem of generalized sampling and reconstruction of finite-rate-of-innovation signals. Specifically, we consider the problem of sampling streams of Dirac impulses and propose a two-channel method that enables fast, local reconstruction und ...

In this paper, we reconstruct signals from underdetermined linear measurements where the componentwise gains of the measurement system are unknown a priori. The reconstruction is performed through an adaptation of the message-passing algorithm called adapt ...

Beside the minimizationof the prediction error, two of the most desirable properties of a regression scheme are stability and interpretability. Driven by these principles, we propose continuous-domain formulations for one-dimensional regression problems. I ...

In this paper, we study the Besov regularity of Levy white noises on the d-dimensional torus. Due to their rough sample paths, the white noises that we consider are defined as generalized stochastic fields. We, initially, obtain regularity results for gene ...

Compact support is undoubtedly one of the wavelet properties that is given the greatest weight both in theory and applications. It is usually believed to be essential for two main reasons: (1) to have fast numerical algorithms, and (2) to have good time or space localization properties. Here, we argue that this constraint is unnecessarily restrictive and that fast algorithms and good localization can also be achieved with non-compactly supported basis functions. By dropping the compact support requirement,

Shape segmentation is an active field of research in biomedical imaging. In this context, we present a new parameterization of a snake that is locally refinable. We introduce the possibility of locally increasing the approximation power of the parametric m ...

Measuring the quality of three-dimensional (3D) reconstructed biological macromolecules by transmission electron microscopy is still an open problem. In this article, we extend the applicability of the spectral signal-to-noise ratio (SSNR) to the evaluatio ...

Mitochondria in intact cells maintain low

Na ^{ + }

levels despite the large electrochemical gradient favoring cation influx into the matrix. In addition, they display individual spontaneous transient depolarizations. We report here that individual mit ...

The Riesz transform is a natural multidimensional extension of the Hilbert transform, and it has been the object of study for many years due to its nice mathematical properties. More recently, the Riesz transform and its variants have been used to construc ...

Lipschitz-constrained neural networks have several advantages over unconstrained ones and can be applied to a variety of problems, making them a topic of attention in the deep learning community. Unfortunately, it has been shown both theoretically and empi ...

We propose a new technique to perform nonuniform to uniform grid conversion: first, interpolate using nonuniform splines, then project the resulting function onto a uniform spline space and finally, resample. We derive a closed form solution to the least-squares approximation problem. Our implementation is computationally exact and works for arbitrary sampling rates. We present examples that illustrate advantages of our projection technique over direct interpolation and resampling. The main benefit is the s

In analogy with steerable wavelets, we present a general construction of adaptable tight wavelet frames, with an emphasis on scaling operations. In particular, the derived wavelets can be "dilated" by a procedure comparable to the operation of steering ste ...

We present a new result characterized by an exact integral expression for the approximation error between a probability density and an integer shift invariant estimate obtained from its samples. Unlike the Parzen window estimate, this estimate avoids recomputing the complete probability density for each new sample: only a few coefficients are required making it practical for real-time applications. We also show how to obtain the exact asymptotic behavior of the approximation error when the number of samples

The Continuous Wavelet Transform (CWT) is an effective way to analyze nonstationary signals and to localize and characterize singularities. Fast algorithms have already been developed to compute the CWT at integer time points and dyadic or integer scales. We propose here a new method that is based on a B-spline expansion of both the signal and the analysis wavelet and that allows the CWT computation at arbitrary scales. Its complexity is O(N), where N represents the size of the input signal; in other words,

Michaël Unser

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Multiresolution Moment Filters

Compact Lensless Phase Imager

A New SURE Approach to Image Denoising: Interscale Orthonormal Wavelet Thresholding

Computation of "Best" Interpolants in the Lp Sense

User-Friendly Semiautomated Assembly of Accurate Image Mosaics in Microscopy

Adaptive Regularization For Three-Dimensional Optical Diffraction Tomography

A Method for Generalized Sampling and Reconstruction of Finite-Rate-of-Innovation Signals

Autocalibrated Signal Reconstruction From Linear Measurements Using Adaptive Gamp

Sparsest Univariate Learning Models Under Lipschitz Constraint

On the Besov regularity of periodic Levy noises

Why Restrict Ourselves to Compactly Supported Basis Functions?

Locally Refinable Parametric Snakes

Spectral Signal-to-Noise Ratio and Resolution Assessment of 3D Reconstructions

Spontaneous $ Na ^{ + } $ Transients in Individual Mitochondria of Intact Astrocytes

Decay Properties of Riesz Transforms and Steerable Wavelets

Improving Lipschitz-Constrained Neural Networks by Learning Activation Functions

Non-Uniform to Uniform Grid Conversion Using Least-Squares Splines

On the Continuous Steering of the Scale of Tight Wavelet Frames

Quantitative $ L ^{ 2 } $ Approximation Error of a Probability Density Estimate Given by It Samples

Fast Continuous Wavelet Transform Based on B-Splines