Thanh-An Michel Pham

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

Nonlinear Inverse Problems in Quantitative Phase Imaging

Thanh-An Michel Pham

The topic of this thesis is the development of new algorithmic reconstruction methods for quantitative phase imaging (QPI). In the past decade, advanced QPI has emerged as a valuable tool to study label-free biological samples and uncover their 3D structural information. This unique tool takes advantage of the scattering of light that results from the complex interplay between the incident electromagnetic wave and the specimen of interest. Yet, the reconstruction process presents numerous challenges in part due to the nonlinear nature of light scattering.In this thesis, we investigate an accurate nonlinear wave-propagation model that relies on the Lippmann-Schwinger (LiSc) equation and apply it to 3D QPI within a variational framework. Our first contribution is a proper discretization of LiSc and a computationally efficient implementation of the nonlinear model.Using our novel forward model, we formulate an inverse-scattering problem within a modern variational framework and solve it to recover the 3D refractive-index (RI) map of a sample when the measurements are complex-valued. In such a setting, the sample is probed with a series of tilted incident waves, while the complex-valued waves are recorded for each illumination. Our algorithmic reconstruction involves a nontrivial proximal gradient-based iterative scheme that requires the Jacobian matrix of the nonlinear operator, for which we are able to derive an explicit expression. By accounting for multiple scattering and adding suitable prior knowledge, our results show that we significantly improve the quality of reconstruction over the state of the art.We then adapt our LiSc model to intensity-only measurements, which has the advantage of simplifying the acquisition setup. We solve this harder inverse problem by leveraging recent advances in proximal algorithms. Our method obtains RI maps with a quality similar to that obtained from complex measurements.Finally, we propose an extension of single-molecule localization microscopy. This modality delivers nanoscale resolution by sequentially activating a subset of fluorescent labels and by extracting their superresolved position. The emission patterns of each label can be distorted by the sample, which reduces the localization accuracy if not accounted for. Here, we exploit those sample-induced aberrations to recover the RI map. We propose an optimization framework in which we reconstruct the RI map using LiSc and optimize the label positions in a joint fashion. Our results show that we effectively recover the RI map of the sample and further improve the localization.

EPFL2022

Diffraction Tomography from Single-Molecule Localization Microscopy: Numerical Feasibility

Thanh-An Michel Pham, Emmanuel Emilien Louis Soubies, Ferréol Arnaud Marie Soulez, Michaël Unser

Single-molecule localization microscopy (SMLM) is a fluorescence microscopy technique that achieves super-resolution imaging by sequentially activating and localizing random sparse subsets of fluorophores. Each activated fluorophore emits light that then scatters through the sample, thus acting as a source of illumination from inside the sample. Hence, the sequence of SMLM frames carries information on the distribution of the refractive index of the sample. In this proof-of-concept work, we explore the possibility of exploiting this information to recover the refractive index of the imaged sample, given the localized molecules. Our results with simulated data suggest that it is possible to exploit the phase information that underlies the SMLM data.

IEEE2021

Optical diffraction tomography from single-molecule localization microscopy

Thanh-An Michel Pham, Emmanuel Emilien Louis Soubies, Ferréol Arnaud Marie Soulez, Michaël Unser

Single-molecule localization microscopy (SMLM) is a powerful method for the imaging of cellular structures. This modality delivers nanoscale resolution by sequentially activating a subset of fluorescent molecules and by extracting their super-resolved positions from the microscope images. The emission patterns of individual molecules can be distorted by the refractive-index (RI) map of the sample, which reduces the accuracy of the molecule localization if not accounted for. In this work, we show that one can exploit those sample-induced aberrations to reveal the structural information of the specimen. Our work is related to the optical diffraction tomography in that we aim to recover the RI map. To that end, we propose an optimization framework in which we reconstruct the RI map and optimize the positions of the molecules in a joint fashion. The benefits of our method are twofold. On one side, we effectively recover the RI map of the sample. On the other side, we further improve the molecule localization—the primary purpose of SMLM. We validate our joint-optimization framework on simulated data. Our results lay the foundation of an exciting and novel extension of SMLM.

2021

Robust Phase Unwrapping via Deep Image Prior for Quantitative Phase Imaging

Nathalie Brandenberg, Matthias Lütolf, Thanh-An Michel Pham, Michaël Unser, Fangshu Yang

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 computational process that recovers a more informative image. It is particularly challenging with thick and complex samples such as organoids. Recent works that rely on supervised training show that deep learning is a powerful method to unwrap the phase; however, supervised approaches require large and representative datasets which are difficult to obtain for complex biological samples. Inspired by the concept of deep image priors, we propose a deep-learning-based method that does not need any training set. Our framework relies on an untrained convolutional neural network to accurately unwrap the phase while ensuring the consistency of the measurements. We experimentally demonstrate that the proposed method faithfully recovers the phase of complex samples on both real and simulated data. Our work paves the way to reliable phase imaging of thick and complex samples with QPI.

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

Adaptive Regularization For Three-Dimensional Optical Diffraction Tomography

Ahmed Ayoub, Thanh-An Michel Pham, Demetri Psaltis, Emmanuel Emilien Louis Soubies, Michaël Unser

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 and speckle noise, the quality of ODT reconstructions is usually better in lateral planes than in the axial direction. In this work, we propose an adaptive regularization to mitigate this issue. We first learn a dictionary from the lateral planes of an initial reconstruction that is obtained with a total-variation regularization. This dictionary is then used to enhance both the lateral and axial planes within a final reconstruction step. The proposed pipeline is validated on real data using an accurate nonlinear forward model. Comparisons with standard reconstructions are provided to show the benefit of the proposed framework.

IEEE2020

Deep-learning projector for optical diffraction tomography

Harshit Gupta, Thanh-An Michel Pham, Michaël Unser, Fangshu Yang

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 derived by the minimization of an objective function in which the data-fidelity term encourages measurement consistency while the regularization term enforces prior constraints. In this work, we propose to train a convolutional neural network (CNN) as the projector in a projected-gradient-descent method. We iteratively produce high-quality estimates and ensure measurement consistency, thus keeping the best of CNN-based and regularization-based worlds. Our experiments on two-dimensional-simulated and real data show an improvement over other conventional or deep-learning-based methods. Furthermore, our trained CNN projector is general enough to accommodate various forward models for the handling of multiple-scattering events. (C) 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

OPTICAL SOC AMER2020

Thanh-An Michel Pham

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

Bayesian Inversion for Nonlinear Imaging Models Using Deep Generative Priors

Nonlinear Inverse Problems in Quantitative Phase Imaging

Diffraction Tomography from Single-Molecule Localization Microscopy: Numerical Feasibility

Optical diffraction tomography from single-molecule localization microscopy

Robust Phase Unwrapping via Deep Image Prior for Quantitative Phase Imaging

A method for assessing the fidelity of optical diffraction tomography reconstruction methods using structured illumination

Adaptive Regularization For Three-Dimensional Optical Diffraction Tomography

Deep-learning projector for optical diffraction tomography

Bayesian Inversion for Nonlinear Imaging Models Using Deep Generative Priors

Nonlinear Inverse Problems in Quantitative Phase Imaging

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

Optical diffraction tomography from single-molecule localization microscopy

Diffraction Tomography from Single-Molecule Localization Microscopy: Numerical Feasibility

Adaptive Regularization For Three-Dimensional Optical Diffraction Tomography

Robust Phase Unwrapping via Deep Image Prior for Quantitative Phase Imaging

A method for assessing the fidelity of optical diffraction tomography reconstruction methods using structured illumination

Deep-learning projector for optical diffraction tomography