UCLA

Three-dimensional image reconstruction is a scientific undertaking of fundamental importance spanning numerous fields including molecular biology, physical chemistry, materials science, physics, and medicine across length scales ranging from the astronomical to the atomic. Despite the broad-reaching nature of this topic, the underlying mechanics and core mathematics are shared, with the ultimate objective being achieving an interpretable representation of some 3D structure from a series of 2D measurements, and, at the time of this writing, at least three Nobel prizes have been awarded for quantitative 3D imaging applications. Although enormous strides have been made over the past several decades in instrumentation, sample preparation, and experimental methodology, comparatively few improvements have been made to tomgraphic reconstruction algorithms. With the ever-increasing availability of high-performance computing resources, a more compelling argument than ever before can be made for the value of developing novel algorithms and the pursuit of accessible scientific software.

In this work, a set of such developments are reported along with several applications. A new tomographic reconstruction algorithm, termed Generalized Fourier Iterative Reconstruction (GENFIRE), is described in detail. By combining powerful, general constraints in both real and reciprocal space, GENFIRE is shown to produce superior reconstructions compared to existing techniques and provides additional benefits including freedom from single-tilt axis restrictions, denoising through a novel Fourier technique termed resolution extension/suppression, and cross-validation through an adapted version of crystallographic $R_{free}$. In subsequent chapters, GENFIRE is applied in a diverse range of experiments including X-ray ptychographic imaging of cells, cryo-electron tomography of bacteria, correlative X-ray fluorescence imaging of algae, and scanning transmission electron microscopy (STEM) of bimetallic nanoparticles at atomic resolution. GENFIRE is fully open-source with a graphical user interface and is freely-available online.

In the appendices, two additional parallel algorithms are described. The first is an optimized graphics processing unit (GPU) implementation of traditional multislice simulation for simulation of STEM image formation as well as the new Plane Wave Reciprocal-space Interpolated Scattering Matrix (PRISM) algorithm that is capable of reducing computation times of routine calculations from several weeks to a few minutes, and the second is a parallel framework for large-scale 3D phase retrieval of symmetric nanostructures from single diffraction patterns.