Jonathan Yuelin Dong

Related publications (4)

Phase Retrieval: From Computational Imaging to Machine Learning: A tutorial

Jonathan Yuelin Dong, Thanh-An Michel Pham, Michaël Unser

Phase retrieval consists in the recovery of a complex-valued signal from intensity-only measurements. As it pervades a broad variety of applications, many researchers have striven to develop phase-retrieval algorithms. Classical approaches involve techniques as varied as generic gradient descent routines or specialized spectral methods, to name a few. However, the phase-recovery problem remains a challenge to this day. Recently, however, advances in machine learning have revitalized the study of phase retrieval in two ways: 1) significant theoretical advances have emerged from the analogy between phase retrieval and single-layer neural networks, and 2) practical breakthroughs have been obtained thanks to deep learning regularization. In this tutorial, we review phase retrieval under a unifying framework that encompasses classical and machine learning methods. We focus on three key elements: applications, an overview of recent reconstruction algorithms, and the latest theoretical results.

2023

Bayesian Inversion for Nonlinear Imaging Models Using Deep Generative Priors

Pakshal Narendra Bohra, Jonathan Yuelin Dong, Thanh-An Michel Pham, Michaël Unser

Most modern imaging systems incorporate a computational pipeline to infer the image of interest from acquired measurements. The Bayesian approach to solve such ill-posed inverse problems involves the characterization of the posterior distribution of the image. It depends on the model of the imaging system and on prior knowledge on the image of interest. In this work, we present a Bayesian reconstruction framework for nonlinear imaging models where we specify the prior knowledge on the image through a deep generative model. We develop a tractable posterior-sampling scheme based on the Metropolis-adjusted Langevin algorithm for the class of nonlinear inverse problems where the forward model has a neural-network-like structure. This class includes most practical imaging modalities. We introduce the notion of augmented deep generative priors in order to suitably handle the recovery of quantitative images. We illustrate the advantages of our framework by applying it to two nonlinear imaging modalities—phase retrieval and optical diffraction tomography.

2022

Interferometric imaging is an emerging technique for particle tracking and mass photometry. Mass or position are estimated from weak signals, coherently scattered from nanoparticles or single molecules, and interfered with a co-propagating reference. In this work, we perform a statistical analysis and derive lower bounds on the measurement precision of the parameters of interest from shot-noise limited images. This is done by computing the classical Cramer-Rao bound (CRB) for localization and mass estimation, using a precise vectorial model of interferometric imaging techniques. We then derive fundamental bounds valid for any imaging system, based on the quantum Cramer-Rao formalism. This approach enables a rigorous and quantitative comparison of common techniques such as interferometric scattering microscopy (iSCAT), coherent brightfield microscopy, and dark-field microscopy. In particular, we demonstrate that the light collection geometry in iSCAT greatly increases the axial position sensitivity, and that the Quantum CRB for mass estimation yields a minimum relative estimation error of sigma(m)/m = 1/(2 root N), where N is the number of collected scattered photons.

IOP PUBLISHING LTD2021

Reservoir Computing meets Recurrent Kernels and Structured Transforms

Jonathan Yuelin Dong, Florent Gérard Krzakala, Ruben Elie Ohana

Reservoir Computing is a class of simple yet efficient Recurrent Neural Networks where internal weights are fixed at random and only a linear output layer is trained. In the large size limit, such random neural networks have a deep connection with kernel methods. Our contributions are threefold: a) We rigorously establish the recurrent kernel limit of Reservoir Computing and prove its convergence. b) We test our models on chaotic time series prediction, a classic but challenging benchmark in Reservoir Computing, and show how the Recurrent Kernel is competitive and computationally efficient when the number of data points remains moderate. c) When the number of samples is too large, we leverage the success of structured Random Features for kernel approximation by introducing Structured Reservoir Computing. The two proposed methods, Recurrent Kernel and Structured Reservoir Computing, turn out to be much faster and more memory-efficient than conventional Reservoir Computing.

Curran Associates, Inc.2020