A Deep Learning Reconstruction Framework for Differential Phase-Contrast Computed Tomography with Incomplete Data

Differential phase-contrast computed tomography (DPC-CT) is a powerful analysis tool for soft-tissue and low-atomic-number samples. Limited by the implementation conditions, DPC-CT with incomplete projections happens quite often. Conventional reconstruction algorithms are not easy to deal with incomplete data. They are usually involved with complicated parameter selection operations, also sensitive to noise and time-consuming. In this paper, we reported a new deep learning reconstruction framework for incomplete data DPC-CT. It is the tight coupling of the deep learning neural network and DPC-CT reconstruction algorithm in the phase-contrast projection sinogram domain. The estimated result is the complete phase-contrast projection sinogram not the artifacts caused by the incomplete data. After training, this framework is determined and can reconstruct the final DPC-CT images for a given incomplete phase-contrast projection sinogram. Taking the sparse-view DPC-CT as an example, this framework has been validated and demonstrated with synthetic and experimental data sets. Embedded with DPC-CT reconstruction, this framework naturally encapsulates the physical imaging model of DPC-CT systems and is easy to be extended to deal with other challengs. This work is helpful to push the application of the state-of-the-art deep learning theory in the field of DPC-CT

Illumination coding meets uncertainty learning: toward reliable AI-augmented phase imaging

We propose a physics-assisted deep learning (DL) framework for large space-bandwidth product (SBP) phase imaging. We design an asymmetric coded illumination scheme to encode high-resolution phase information across a wide field-of-view. We then develop a matching DL algorithm to provide large-SBP phase estimation. We show that this illumination coding scheme is highly scalable in achieving flexible resolution, and robust to experimental variations. We demonstrate this technique on both static and dynamic biological samples, and show that it can reliably achieve 5X resolution enhancement across 4X FOVs using only five multiplexed measurements -- more than 10X data reduction over the state-of-the-art. Typical DL algorithms tend to provide over-confident predictions, whose errors are only discovered in hindsight. We develop an uncertainty learning framework to overcome this limitation and provide predictive assessment to the reliability of the DL prediction. We show that the predicted uncertainty maps can be used as a surrogate to the true error. We validate the robustness of our technique by analyzing the model uncertainty. We quantify the effect of noise, model errors, incomplete training data, and "out-of-distribution" testing data by assessing the data uncertainty. We further demonstrate that the predicted credibility maps allow identifying spatially and temporally rare biological events. Our technique enables scalable AI-augmented large-SBP phase imaging with dependable predictions.Published versio

Automatic Differentiation for Inverse Problems in X-ray Imaging and Microscopy

Computational techniques allow breaking the limits of traditional imaging methods, such as time restrictions, resolution, and optics flaws. While simple computational methods can be enough for highly controlled microscope setups or just for previews, an increased level of complexity is instead required for advanced setups, acquisition modalities or where uncertainty is high; the need for complex computational methods clashes with rapid design and execution. In all these cases, Automatic Differentiation, one of the subtopics of Artificial Intelligence, may offer a functional solution, but only if a GPU implementation is available. In this paper, we show how a framework built to solve just one optimisation problem can be employed for many different X-ray imaging inverse problems

New Algorithms in Computational Microscopy

Microscopy plays an important role in providing tools to microscopically observe objects and their surrounding areas with much higher resolution ranging from the scale between molecular machineries (angstrom) and individual cells (micrometer). Under microscopes, illumination, such as visible light and electron-magnetic radiation/electron beam, interacts with samples, then they are scattered to a plane and are recorded. Computational microscopy corresponds to image reconstruction from these measurements as well as improving quality of the images. Along with the evolution of microscopy, new studies are discovered and algorithms need development not only to provide high-resolution imaging but also to decipher new and advanced research. In this dissertation, we focus on algorithm development for inverse problems in microscopy, specifically phase retrieval and tomography, and the application of these techniques to machine learning. The four studies in this dissertation demonstrates the use of optimization and calculus of variation in imaging science and other different disciplines.Study 1 focuses on coherent diffractive imaging (CDI) or phase retrieval, a non-linear inverse problem that aims to recover 2D image from it Fourier transforms in modulus taking into account that extra information provided by oversampling as a second constraint. To solve this two-constraint minimization, we proceed from Hamilton-Jacobi partial differential equation (HJ-PDE) and its Hopf-Lax formula. Introducing generalized Bregman distance to the HJ-PDE and applying Legendre transform, we derive our generalized proximal smoothing (GPS) algorithm under the form of primal-dual hybrid gradient (PDHG). While the reflection operator, known as extrapolating momentum, helps overcome local minima, the smoothing by the generalized Bregman distance is adjusted to improve convergence and consistency of phase retrieval.Study 2 focuses on electron tomography, 3D image reconstruction from a set of 2D projections obtained from a transmission electron microscope (TEM) or X-ray microscope. Notice that current tomography algorithms limit to a single tilt axis and fail to work with fully or partially missing data. In the light of calculus of variations and Fourier slice theorem (FST), we develop a highly accurate tomography iterative algorithm that can provide higher resolution imaging and work with missing data as well as has capability to perform multiple-tilt-axis tomography. The algorithm is further developed to work with non-isolated objects and partially-blocked projections which have become more popular in experiment. The success of real space iterative reconstruction engine (RESIRE) opens a new era to the study of tomography in material science and magnetic structures (vector Tomography).Study 3 and 4 are applications of our algorithms to machine learning. Study 3 develops a backward Euler method in a stochastic manner to solve K-mean clustering, a well-known non-convex optimization problem. The algorithm has been shown to improve minimums and consistency, providing a new powerful tool to the class of classification techniques. Study 4 is a direct application of GPS to deep learning gradient descent algorithms. Linearizing the Hopf-Lax formula derived in GPS, we derive our method Laplacian smoothing gradient descent (LSGD), simply known as gradient smoothing. Our experiment shows that LSGD has the ability to search for better and flatter minimums, reduce variation, and obtain higher accuracy and consistency