Thanh-an Pham

Pakshal Bohra, Thanh-an Pham, Jonathan Dong et al.

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.

Yan Liu, Jonathan Dong, Thanh-An Pham et al.

Optical projection tomography (OPT) is a powerful tool for biomedical studies. It achieves 3D visualization of mesoscopic biological samples with high spatial resolution using conventional tomographic-reconstruction algorithms. However, various artifacts degrade the quality of the reconstructed images due to experimental imperfections in the OPT instruments. While many efforts have been made to characterize and correct for these artifacts, they focus on one specific type of artifacts. This work has two contributions. First, we systematically document a catalog of mechanical artifacts based on a 3D description of the imaging system that uses a set of angular and translational parameters. Then, we introduce a calibration algorithm that recovers the unknown system parameters fed into the final 3D iterative reconstruction algorithm for a distortion-free volumetric image. Simulations with beads data and experimental results on a fluorescent textile fiber confirm that our algorithm successfully removes miscalibration artifacts in the reconstruction.

Quentin Denoyelle, Thanh-an Pham, Pol del Aguila Pla et al.

We propose the use of Flat Metric to assess the performance of reconstruction methods for single-molecule localization microscopy (SMLM) in scenarios where the ground-truth is available. Flat Metric is intimately related to the concept of optimal transport between measures of different mass, providing solid mathematical foundations for SMLM evaluation and integrating both localization and detection performance. In this paper, we provide the foundations of Flat Metric and validate this measure by applying it to controlled synthetic examples and to data from the SMLM 2016 Challenge.