Michaël Unser
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View article: Revisiting PSF models: Unifying framework and high‐performance implementation
Revisiting PSF models: Unifying framework and high‐performance implementation Open
Localisation microscopy often relies on detailed models of point‐spread functions. For applications such as deconvolution or PSF engineering, accurate models for light propagation in imaging systems with a high numerical aperture are requi…
View article: Undersampled Phase Retrieval with Image Priors
Undersampled Phase Retrieval with Image Priors Open
Phase retrieval seeks to recover a complex signal from amplitude-only measurements, a challenging nonlinear inverse problem. Current theory and algorithms often ignore signal priors. By contrast, we evaluate here a variety of image priors …
View article: A Statistical Benchmark for Diffusion Posterior Sampling Algorithms
A Statistical Benchmark for Diffusion Posterior Sampling Algorithms Open
We propose a statistical benchmark for diffusion posterior sampling (DPS) algorithms for Bayesian linear inverse problems. The benchmark synthesizes signals from sparse Lévy-process priors whose posteriors admit efficient Gibbs methods. Th…
View article: Perturbative Fourier ptychographic microscopy for fast quantitative phase imaging
Perturbative Fourier ptychographic microscopy for fast quantitative phase imaging Open
In computational phase imaging with a microscope equipped with an array of light emitting diodes as the illumination unit, conventional Fourier ptychographic microscopy achieves high resolution and wide-field reconstructions but is constra…
View article: Multivariate Fields of Experts
Multivariate Fields of Experts Open
We introduce the multivariate fields of experts, a new framework for the learning of image priors. Our model generalizes existing fields of experts methods by incorporating multivariate potential functions constructed via Moreau envelopes …
View article: Adaptive Vector-Valued Splines for the Resolution of Inverse Problems
Adaptive Vector-Valued Splines for the Resolution of Inverse Problems Open
We introduce a general framework for the reconstruction of vector-valued functions from finite and possibly noisy data, acquired through a known measurement operator. The reconstruction is done by the minimization of a loss functional form…
View article: The Gaussian Latent Machine: Efficient Prior and Posterior Sampling for Inverse Problems
The Gaussian Latent Machine: Efficient Prior and Posterior Sampling for Inverse Problems Open
We consider the problem of sampling from a product-of-experts-type model that encompasses many standard prior and posterior distributions commonly found in Bayesian imaging. We show that this model can be easily lifted into a novel latent …
View article: Generalized Ray Tracing with Basis functions for Tomographic Projections
Generalized Ray Tracing with Basis functions for Tomographic Projections Open
This work aims at the precise and efficient computation of the x-ray projection of an image represented by a linear combination of general shifted basis functions that typically overlap. We achieve this with a suitable adaptation of ray tr…
View article: Convergence analysis of the discretization of continuous-domain inverse problems
Convergence analysis of the discretization of continuous-domain inverse problems Open
We study continuous-domain linear inverse problems that involve a general data-fidelity term and a regularisation term. We consider a regularisation that is formed by the sparsity-promoting total-variation norm, pre-composed with a differe…
View article: DEALing with Image Reconstruction: Deep Attentive Least Squares
DEALing with Image Reconstruction: Deep Attentive Least Squares Open
State-of-the-art image reconstruction often relies on complex, highly parameterized deep architectures. We propose an alternative: a data-driven reconstruction method inspired by the classic Tikhonov regularization. Our approach iterativel…
View article: Comparison of 2D Regular Lattices for the CPWL Approximation of Functions
Comparison of 2D Regular Lattices for the CPWL Approximation of Functions Open
We investigate the approximation error of functions with continuous and piecewise-linear (CPWL) representations. We focus on the CPWL search spaces generated by translates of box splines on two-dimensional regular lattices. We compute the …
View article: Revisiting PSF models: unifying framework and high-performance implementation
Revisiting PSF models: unifying framework and high-performance implementation Open
Localization microscopy often relies on detailed models of point spread functions. For applications such as deconvolution or PSF engineering, accurate models for light propagation in imaging systems with high numerical aperture are require…
View article: Model-based temporal unmixing towards quantitative photo-switching optoacoustic tomography
Model-based temporal unmixing towards quantitative photo-switching optoacoustic tomography Open
Optoacoustic (OA) imaging combined with reversibly photoswitchable proteins has emerged as a promising technology for the high-sensitivity and multiplexed imaging of cells in live tissues in preclinical research. Through carefully designed…
View article: Learning of Patch-Based Smooth-Plus-Sparse Models for Image Reconstruction
Learning of Patch-Based Smooth-Plus-Sparse Models for Image Reconstruction Open
We aim at the solution of inverse problems in imaging, by combining a penalized sparse representation of image patches with an unconstrained smooth one. This allows for a straightforward interpretation of the reconstruction. We formulate t…
View article: Point-Spread-Function Engineering in MINFLUX: Optimality of Donut and Half-Moon Excitation Patterns
Point-Spread-Function Engineering in MINFLUX: Optimality of Donut and Half-Moon Excitation Patterns Open
Localization microscopy enables imaging with resolutions that surpass the conventional optical diffraction limit. Notably, the MINFLUX method achieves super-resolution by shaping the excitation point-spread function (PSF) to minimize the r…
View article: Structured Random Model for Fast and Robust Phase Retrieval
Structured Random Model for Fast and Robust Phase Retrieval Open
Phase retrieval, a nonlinear problem prevalent in imaging applications, has been extensively studied using random models, some of which with i.i.d. sensing matrix components. While these models offer robust reconstruction guarantees, they …
View article: Controlled Learning of Pointwise Nonlinearities in Neural-Network-Like Architectures
Controlled Learning of Pointwise Nonlinearities in Neural-Network-Like Architectures Open
We present a general variational framework for the training of freeform nonlinearities in layered computational architectures subject to some slope constraints. The regularization that we add to the traditional training loss penalizes the …
View article: Parseval Convolution Operators and Neural Networks
Parseval Convolution Operators and Neural Networks Open
We first establish a kernel theorem that characterizes all linear shift-invariant (LSI) operators acting on discrete multicomponent signals. This result naturally leads to the identification of the Parseval convolution operators as the cla…
View article: Surpassing light inhomogeneities in structured‐illumination microscopy with FlexSIM
Surpassing light inhomogeneities in structured‐illumination microscopy with FlexSIM Open
Super‐resolution structured‐illumination microscopy (SIM) is a powerful technique that allows one to surpass the diffraction limit by up to a factor two. Yet, its practical use is hampered by its sensitivity to imaging conditions which mak…
View article: Iteratively Refined Image Reconstruction with Learned Attentive Regularizers
Iteratively Refined Image Reconstruction with Learned Attentive Regularizers Open
We propose a regularization scheme for image reconstruction that leverages the power of deep learning while hinging on classic sparsity-promoting models. Many deep-learning-based models are hard to interpret and cumbersome to analyze theor…
View article: Iteratively Refined Image Reconstruction with Learned Attentive Regularizers
Iteratively Refined Image Reconstruction with Learned Attentive Regularizers Open
We propose a regularization scheme for image reconstruction that leverages the power of deep learning while hinging on classic sparsity-promoting models. Many deep-learning-based models are hard to interpret and cumbersome to analyze theor…
View article: A Continuous-Domain Solution for Computed Tomography with Hessian Total-Variation Regularization
A Continuous-Domain Solution for Computed Tomography with Hessian Total-Variation Regularization Open
We formulate computed-tomography reconstruction as a continuous-domain optimization problem with Hessian total variation (HTV) as the regularizer. HTV is a sparsity-promoting regularizer that favors continuous and piecewise-linear function…
View article: Model-based temporal unmixing towards quantitative photo-switching optoacoustic tomography
Model-based temporal unmixing towards quantitative photo-switching optoacoustic tomography Open
Optoacoustic (OA) imaging combined with reversibly photoswitchable proteins has emerged as a promising technology for the high-sensitivity and multiplexed imaging of cells in live tissues in preclinical research. Through carefully-designed…
View article: Random ReLU Neural Networks as Non-Gaussian Processes
Random ReLU Neural Networks as Non-Gaussian Processes Open
We consider a large class of shallow neural networks with randomly initialized parameters and rectified linear unit activation functions. We prove that these random neural networks are well-defined non-Gaussian processes. As a by-product, …
View article: A CODE-BASED DISTRIBUTED GRADIENT DESCENT SCHEME FOR DECENTRALIZED CONVEX OPTIMIZATION
A CODE-BASED DISTRIBUTED GRADIENT DESCENT SCHEME FOR DECENTRALIZED CONVEX OPTIMIZATION Open
In this paper, we consider a large network containing many regions such that each region is equipped with a worker with some data processing and communication capability.For such a network, some workers may become stragglers due to the fai…
View article: Sensitivity-Aware Density Estimation in Multiple Dimensions
Sensitivity-Aware Density Estimation in Multiple Dimensions Open
We formulate an optimization problem to estimate probability densities in the context of multidimensional problems that are sampled with uneven probability. It considers detector sensitivity as an heterogeneous density and takes advantage …