Publications by Michaël Unser

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Interpolation is the means by which a continuously defined model is fit to discrete data samples. When the data samples are exempt of noise, it seems desirable to build the model by fitting them exactly. In medical imaging, where quality is of paramount im ...

Optical diffraction tomography is an effective tool to estimate the refractive indices of unknown objects. It proceeds by solving an ill-posed inverse problem for which the wave equation governs the scattering events. The solution has traditionally been de ...

I. Introduction Wavelets are the result of collective efforts that recognized common threads between ideas and concepts that had been independently developed and investigated by distinct research communities. They provide a unifying framework for decomposing images, volumes, and time-series data into their elementary constituents across scale. Although a relatively recent construct, wavelets have become a tool of choice for engineers, physicists, and mathematicians, leading to efficient solutions in time a

Motivated by the fractal-like behavior of natural images, we develop a smoothing technique that uses a regularization functional which is a fractional iterate of the Laplacian. This type of functional was initially introduced by Duchon for the approximatio ...

This paper addresses the task of learning convex regularizers to guide the reconstruction of images from limited data. By imposing that the reconstruction be amplitude-equivariant, we narrow down the class of admissible functionals to those that can be expressed as a power of a seminorm. We then show that such functionals can be approximated to arbitrary precision with the help of polyhedral norms. In particular, we identify two dual parameterizations of such systems: (i) a synthesis (or atomic) form with a

We analyze the representation of periodic signals in a scaling function basis. This representation is sufficiently general to include the widely used approximation schemes like wavelets, splines and Fourier series representation. We derive a closed form expression for the approximation error in the scaling function representation. The error formula takes the simple form of a Parseval like sum, weighted by an appropriate error kernel. This formula may be useful in choosing the right representation for a clas

Modeling the acoustical process of soft biological tissue imaging and understanding the consequences of the approximations required by. such modeling are key steps for accurately simulating ultrasonic scanning as well as estimating the scattering coefficie ...

We provide a generic framework to learn shape dictionaries of landmark-based curves that are defined in the continuous domain. We first present an unbiased alignment method that involves the construction of a mean shape as well as training sets whose eleme ...

Generalized sampling consists in the recovery of a function f, from the samples of the responses of a collection of linear shift-invariant systems to the input f . The reconstructed function is typically a member of a finitely generated integer-shift invar ...

We present CryoGAN, a new paradigm for single-particle cryo-electron microscopy (cryo-EM) reconstruction based on unsupervised deep adversarial learning. In single-particle cryo-EM, the structure of a biomolecule needs to be reconstructed from a large set ...

The quantitative assessment of cardiac motion is a fundamental concept to evaluate ventricular malfunction. We present a new optical-flow-based method for estimating heart motion from two-dimensional echocardiographic sequences. To account for typical hear ...

Quantitative phase imaging (QPI) refers to label-free techniques that produce images containing morphological information. In this chapter, we focus on 2D phase imaging with a holographic setup. In such a setting, the complex-valued measurements contain both intensity and phase information. The phase is related to the distribution of the refractive index of the underlying specimen. In practice, the collected phase happens to be wrapped (i.e., modulo 2π of the original phase) and one gains quantitative infor

Digital analysis and processing of signals inherently relies on the existence of methods for reconstructing a continuous-time signal from a sequence of corrupted discrete-time samples. In this paper, a general formulation of this problem is developed that ...

We introduce an adaptive continuous-domain modeling approach to texture and natural images. The continuous-domain image is assumed to be a smooth function, and we embed it in a parameterized Sobolev space. We point out a link between Sobolev spaces and sto ...

Wavelet-based methods have become most popular for the compression of two-dimensional medical images and sequences. The standard implementations consider data sizes that are powers of two. There is also a large body of literature treating issues such as the choice of the "optimal" wavelets and the performance comparison of competing algorithms. With the advent of telemedicine, there is a strong incentive to extend these techniques to higher dimensional data such as dynamic three-dimensional (3-D) echocardio

We introduce a variational framework to learn the activation functions of deep neural networks. Our aim is to increase the capacity of the network while controlling an upper-bound of the actual Lipschitz constant of the input-output relation. To that end, ...

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 ...

In this paper, we propose a novel deep convolutional neural network (CNN)-based algorithm for solving ill-posed inverse problems. Regularized iterative algorithms have emerged as the standard approach to ill-posed inverse problems in the past few decades. ...

Model-based statistical analysis of functional magnetic resonance imaging (fMRI) data relies on the general linear model and statistical hypothesis testing. Due to the large number of intracranial voxels, it is important to deal with the multiple compariso ...

We propose a novel unsupervised deep-learning-based algorithm for dynamic magnetic resonance imaging (MRI) reconstruction. Dynamic MRI requires rapid data acquisition for the study of moving organs such as the heart. We introduce a generalized version of t ...

Michaël Unser

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Regularized Interpolation for Noisy Images

Deep-learning projector for optical diffraction tomography

Guest Editorial: Wavelets in Medical Imaging

Polyharmonic Smoothing Splines and the Multidimensional Wiener Filtering of Fractal-Like Signals

Universal Architectures for the Learning of Polyhedral Norms and Convex Regularizers

An Error Analysis for the Sampling of Periodic Signals

A bulk modulus dependent linear model for acoustical imaging

Landmark-Based Shape Encoding and Sparse-Dictionary Learning in the Continuous Domain

Shortest-support multi-spline bases for generalized sampling

CryoGAN: A New Reconstruction Paradigm for Single-Particle Cryo-EM Via Deep Adversarial Learning

Myocardial Motion Analysis from B-Mode Echocardiograms

Regularizing Neural Network for Phase Unwrapping

Nonideal Sampling and Interpolation from Noisy Observations in Shift-Invariant Spaces

Adaptive Image Resizing Based on Continuous-Domain Stochastic Modeling

Four-Dimensional Wavelet Compression of Arbitrarily Sized Echocardiographic Data

Deep Neural Networks With Trainable Activations and Controlled Lipschitz Constant

Reconstruction Of Biomedical Images And Sparse Stochastic Modeling

Deep Convolutional Neural Network for Inverse Problems in Imaging

False Discovery Rate for Wavelet-Based Statistical Parametric Mapping

Time-Dependent Deep Image Prior for Dynamic MRI