Publications by Michaël Unser

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Rectified-linear-unit (ReLU) neural networks, which play a prominent role in deep learning, generate continuous and piecewise-linear (CPWL) functions. While they provide a powerful parametric representation, the mapping between the parameter and function s ...

This paper is devoted to the characterization of an extended family of continuous-time autoregressive moving average (CARMA) processes that are solutions of stochastic differential equations driven by white Levy innovations. These are completely specified ...

This paper presents an account of the current state of sampling, 50 years after Shannon's formulation of the sampling theorem. The emphasis is on regular sampling where the grid is uniform. This topic has benefited from a strong research revival during the past few years, thanks in part to the mathematical connections that were made with wavelet theory. To introduce the reader to the modern, Hilbert-space formulation, we re-interpret Shannon's sampling procedure as an orthogonal projection onto the subspace

We present a multilevel extension of the popular "thresholded Landweber" algorithm for wavelet-regularized image restoration that yields an order of magnitude speed improvement over the standard fixed-scale implementation. The method is generic and targete ...

We focus on the generalized-interpolation problem. There, one reconstructs continuous-domain signals that honor discrete data constraints. This problem is infinite-dimensional and ill-posed. We make it well-posed by imposing that the solution balances data ...

We consider

L ^{ 1 }

-TV regularization of univariate signals with values on the real line or on the unit circle. While the real data space leads to a convex optimization problem, the problem is nonconvex for circle-valued data. In this paper, we deriv ...

A critical role of circadian oscillators in orchestrating insulin secretion and islet gene transcription has been demonstrated recently. However, these studies focused on whole islets and did not explore the interplay between α-cell and β-cell clocks. We p ...

Quantitative phase imaging (QPI) is an emerging label-free technique that produces images containing morphological and dynamical information without contrast agents. Unfortunately, the phase is wrapped in most imaging system. Phase unwrapping is the comput ...

We formulate the tomographic reconstruction problem in a variational setting. The object to be reconstructed is considered as a continuous density function, unlike in the pixel-based approaches. The measurements are modeled as linear operators (Radon transform), integrating the density function along the ray path. The criterion that we minimize consists of a data term and a regularization term. The data term represents the inconsistency between applying the measurement model to the density function and the

Bayesian estimation problems involving Gaussian distributions often result in linear estimation techniques. Nevertheless, there are no general statements as to whether the linearity of the Bayesian estimator is restricted to the Gaussian case. The two comm ...

We present a new method for estimating heart motion from two-dimensional (2D) echocardiographic sequences. It is inspired by the Lucas-Kanade algorithm for optical flow which estimates motion parameters over a sliding window. However, instead of assuming that the motion is constant within the analysis window, we consider a model that is locally affine and can account for typical heart motions such as dilation/contraction and shear. Another refinement is spatial adaptivity which is achieved by estimating dis

Our main goal in this paper is to set the foundations of a general continuous-domain framework for designing steerable, reversible signal transformations (a.k.a. frames) in multiple dimensions (d ≥ 2). To that end, we introduce a self-reversible, Nth-order ...

Regularization addresses the ill-posedness of the training problem in machine learning or the reconstruction of a signal from a limited number of measurements. The method is applicable whenever the problem is formulated as an optimization task. The standar ...

Optical diffraction tomography (ODT) can be described using the scattering process through an inhomogeneous media. An inherent nonlinearity exists relating the scattering medium and the scattered field due to multiple scattering. Multiple scattering is oft ...

We introduce an extended family of continuous-domain stochastic models for sparse, piecewise-smooth signals. These are specified as solutions of stochastic differential equations, or, equivalently, in terms of a suitable innovation model; the latter is ana ...

Existing shape models with spherical topology are typically designed either in the discrete domain using interpolating polygon meshes or in the continuous domain using smooth but non-interpolating schemes such as subdivision or NURBS. Both polygon models a ...

Compressed sensing can substantially reduce the number of samples required for conventional signal acquisition at the expense of an additional reconstruction procedure. It also provides robust reconstruction when using quantized measurements, including in ...

Sinusoidal transforms such as the DCT are known to be optimal-that is, asymptotically equivalent to the Karhunen-Loeve transform (KLT)-for the representation of Gaussian stationary processes, including the classical AR(1) processes. While the KLT remains a ...

Fourier ptychography (FP) involves the acquisition of several low-resolution intensity images of a sample under varying illumination angles. They are then combined into a high-resolution complex-valued image by solving a phase-retrieval problem. The object ...

In our recent work, the sampling and reconstruction of non-decaying signals, modeled as members of weighted-L-p spaces, were shown to be stable with an appropriate choice of the generating kernel for the shift-invariant reconstruction space. In this paper, ...

Michaël Unser

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Stable parameterization of continuous and piecewise-linear functions

A Unified Formulation of Gaussian Versus Sparse Stochastic Processes-Part II: Discrete-Domain Theory

Sampling—50 Years After Shannon

A Fast Multilevel Algorithm for Wavelet-Regularized Image Restoration

Continuous-Domain Signal Reconstruction Using L-p-Norm Regularization

Exact Algorithms for $ L ^{ 1 } $ -TV Regularization of Real-Valued or Circle-Valued Signals

Pancreatic α- and β-Cellular Clocks Have Distinct Molecular Properties and Impact on Islet Hormone Secretion and Gene Expression

Robust Phase Unwrapping via Deep Image Prior for Quantitative Phase Imaging

Variational Approach to Tomographic Reconstruction

On the Linearity of Bayesian Interpolators for Non-Gaussian Continuous-Time AR(1) Processes

Motion Analysis of Echocardiograms Using a Local-Affine, Spatio-Temporal Model

Wavelet Steerability and the Higher-Order Riesz Transform

A Unifying Representer Theorem for Inverse Problems and Machine Learning

Imaging complex objects using learning tomography

Stochastic Models for Sparse and Piecewise-Smooth Signals

Smooth Shapes with Spherical Topology: Beyond Traditional Modeling, Efficient Deformation, and Interaction

Binary Compressed Imaging

On The Optimality Of Operator-Like Wavelets For Sparse Ar(1) Processes

Dynamic Fourier ptychography with deep spatiotemporal priors

Approximation of Non-decaying Signals from Shift-Invariant Subspaces