Image recovery from rotational and translational invariants

We introduce a framework for recovering an image from its rotationally and translationally invariant features based on autocorrelation analysis. This work is an instance of the multi-target detection statistical model, which is mainly used to study the mathematical and computational properties of single-particle reconstruction using cryo-electron microscopy (cryo-EM) at low signal-to-noise ratios. We demonstrate with synthetic numerical experiments that an image can be reconstructed from rotationally and translationally invariant features and show that the reconstruction is robust to noise. These results constitute an important step towards the goal of structure determination of small biomolecules using cryo-EM.Comment: 5 pages, 3 figure

Multi-target detection with rotations

We consider the multi-target detection problem of estimating a two-dimensional target image from a large noisy measurement image that contains many randomly rotated and translated copies of the target image. Motivated by single-particle cryo-electron microscopy, we focus on the low signal-to-noise regime, where it is difficult to estimate the locations and orientations of the target images in the measurement. Our approach uses autocorrelation analysis to estimate rotationally and translationally invariant features of the target image. We demonstrate that, regardless of the level of noise, our technique can be used to recover the target image when the measurement is sufficiently large.Comment: 20 pages, 5 figure

Coherent diffraction of single Rice Dwarf virus particles using hard X-rays at the Linac Coherent Light Source

Single particle diffractive imaging data from Rice Dwarf Virus (RDV) were recorded using the Coherent X-ray Imaging (CXI) instrument at the Linac Coherent Light Source (LCLS). RDV was chosen as it is a wellcharacterized model system, useful for proof-of-principle experiments, system optimization and algorithm development. RDV, an icosahedral virus of about 70 nm in diameter, was aerosolized and injected into the approximately 0.1 mu m diameter focused hard X-ray beam at the CXI instrument of LCLS. Diffraction patterns from RDV with signal to 5.9 angstrom ngstrom were recorded. The diffraction data are available through the Coherent X-ray Imaging Data Bank (CXIDB) as a resource for algorithm development, the contents of which are described here.11Ysciescopu

Dragonfly

Single-particle imaging (SPI) with X-ray free-electron lasers has the potential to change fundamentally how biomacromolecules are imaged. The structure would be derived from millions of diffraction patterns, each from a different copy of the macromolecule before it is torn apart by radiation damage. The challenges posed by the resultant data stream are staggering: millions of incomplete, noisy and un-oriented patterns have to be computationally assembled into a three-dimensional intensity map and then phase reconstructed. In this paper, the Dragonfly software package is described, based on a parallel implementation of the expand-maximize-compress reconstruction algorithm that is well suited for this task. Auxiliary modules to simulate SPI data streams are also included to assess the feasibility of proposed SPI experiments at the Linac Coherent Light Source, Stanford, California, USA

Orientation reconstruction algorithms for X-ray serial diffraction data

Due to irreversible radiation damage, structure determination of biological macromolecules using X-rays is often done by taking snapshots from individual copies of the sample and assembling the snapshots in the end to solve the 3D structures. It is difficult to control the orientations of micron or sub-micron sized specimens when delivered to the X-ray beam. Furthermore, the signals in the snapshots may be so weak that each of them cannot be oriented separately. This thesis develops algorithms to address the task of 3D reconstruction from unoriented, noisy snapshots, with special focus on two X-ray methods. For the first one, single particle imagining at X-ray free electron lasers, we discuss the difficulty of orientation reconstruction of samples through computer simulation, and then present the analysis results of two experimental datasets. For the second technique, serial microcrystallography at synchrotron storage ring sources, we first describe the development of our reconstruction algorithm through two proof-of-concept studies. In these studies, diffraction patterns were collected from large protein crystals to simulate the signal level of those collected from protein microcrystals at storage ring sources. Finally, we demonstrate our method by solving a protein structure from microcrystal diffraction patterns collected at a storage ring synchrotron source. These data would have been discarded by crystallographers because of their weak signals. Through the detailed presentation of the analysis processes, this thesis is also meant to be a self-contained tutorial on reconstruction problems using X-ray sources

“Gibasis pellucida” (Martens & Galeotti) D.R. Hunt (Commelinaceae), A Newly Naturalized Plant in Taiwan

Commelinaceae is a monocot family mainly distributed in tropical and temperate region. Several naturalized species were recorded in Taiwan these years. Recently we found a newly naturalized species-＂Gibasis pellucida＂ (Martens & Galeotti) D.R. Hunt in Northern Taiwan. This species was native to Mexico, and introduced as ornamental plant in many countries. This is a newly naturalized species and genus for Flora of Taiwan. Line drawing, photos and distribution map were provided in this study. Finally, we revised naturalized species of Commelinaceae in Taiwan, the naturalization of them were related to ornamental activity, some species had set up large population already, especially the Tradescantia species. Thus we need pay more attention to these potentially invasive plants.鴨跖草科為熱帶常見的單子葉草本植物，之前多位學者已相繼報導數種本科的馴化植物。最近作者等又於臺灣北部發現一種新馴化植物，經查為原產於墨西哥之細梗鴨跖草。本種為一園藝觀賞植物，無性繁殖容易且適應力強，推測是人為引進而逸出於野外。根據這幾年野外的調查發現其野外族群數量有穩定成長，未來動態值得注意。對台灣的植物誌而言，細梗鴨跖草屬與細梗鴨跖草均為本島的新記錄