Joanna Klukowska

SNARK09 - A software package for reconstruction of 2D images from 1D projections

The problem of reconstruction of slices and volumes from 1D and 2D projections has arisen in a large number of scientific fields (including computerized tomography, electron microscopy, X-ray microscopy, radiology, radio astronomy and holography). Many different methods (algorithms) have been suggested for its solution. In this paper we present a software package, SNARK09, for reconstruction of 2D images from their 1D projections. In the area of image reconstruction, researchers often desire to compare two or more reconstruction techniques and assess their relative merits. SNARK09 provides a uniform framework to implement algorithms and evaluate their performance. It has been designed to treat both parallel and divergent projection geometries and can either create test data (with or without noise) for use by reconstruction algorithms or use data collected by another software or a physical device. A number of frequently-used classical reconstruction algorithms are incorporated. The package provides a means for easy incorporation of new algorithms for their testing, comparison and evaluation. It comes with tools for statistical analysis of the results and ten worked examples.

Fully three-dimensional defocus-gradient corrected backprojection in cryoelectron microscopy.

Recognizing that the microscope depth of field is a significant resolution-limiting factor in 3D cryoelectron microscopy, Jensen and Kornberg proposed a concept they called defocus-gradient corrected backprojection (DGCBP) and illustrated by computer simulations that DGCBP can effectively eliminate the depth of field limitation. They did not provide a mathematical justification for their concept. Our paper provides this, by showing (in the idealized case of noiseless data being available for all projection directions) that the reconstructions obtained based on DGCBP from data produced with distance-dependent blurring are essentially the same as what is obtained by a classical method of reconstruction of a 3D object from its line integrals. The approach is general enough to be applicable for correcting for any distance-dependent blurring during projection data collection. We present a new implementation of the DGCBP concept, one that closely follows the mathematics of its justifications, and illustrate it using mathematically described phantoms and their reconstructions from finitely many distance-dependently blurred projections.

Morphology of Influenza B/Lee/40 Determined by Cryo-Electron Microscopy

Cryo-electron microscopy projection image analysis and tomography is used to describe the overall architecture of influenza B/Lee/40. Algebraic reconstruction techniques with utilization of volume elements (blobs) are employed to reconstruct tomograms of this pleomorphic virus and distinguish viral surface spikes. The purpose of this research is to examine the architecture of influenza type B virions by cryo-electron tomography and projection image analysis. The aims are to explore the degree of ribonucleoprotein disorder in irregular shaped virions; and to quantify the number and distribution of glycoprotein surface spikes (hemagglutinin and neuraminidase) on influenza B. Projection image analysis of virion morphology shows that the majority (∼83%) of virions are spherical with an average diameter of 134±19 nm. The aspherical virions are larger (average diameter = 155±47 nm), exhibit disruption of the ribonucleoproteins, and show a partial loss of surface protein spikes. A count of glycoprotein spikes indicates that a typical 130 nm diameter type B virion contains ∼460 surface spikes. Configuration of the ribonucleoproteins and surface glycoprotein spikes are visualized in tomogram reconstructions and EM densities visualize extensions of the spikes into the matrix. The importance of the viral matrix in organization of virus structure through interaction with the ribonucleoproteins and the anchoring of the glycoprotein spikes to the matrix is demonstrated.

The soft x-ray transform

Several new forward models are introduced as mathematical formalizations of the processes that take place during image formation in transmission soft x-ray microscopy, which has the unique capability of imaging whole cells in their native environment with high resolution. Mathematical solutions of some of the associated inverse problems are provided by deriving closed-form formulas specifying the inverse transforms. Numerical experimental results are presented to demonstrate how the inverse transforms can be used to improve the reconstructions computed from data acquired according to the forward models.

Finding mobile data: efficiency vs. location inaccuracy

A token is hidden in one out of n boxes following some known probability distribution and then all the boxes are locked. The goal of a searcher is to find the token in at most D ≤ n rounds by opening as few boxes as possible, where in each round any set of boxes may be opened. We design and analyze strategies for a searcher who does not know the exact values of the probabilities associated with the locked boxes. Instead, the searcher might know only the complete order or a partial order of the probabilities, or ranges in which these probabilities fall. We show that with limited information the searcher can find the token without opening significantly more boxes compared to a searcher who has full knowledge. This problem is equivalent to finding mobile users (tokens) in cellular networks (boxes) and finding data (tokens) in sensor networks (boxes).

XTEND: Extending the depth of field in cryo soft X-ray tomography

We have developed a new data collection method and processing framework in full field cryo soft X-ray tomography to computationally extend the depth of field (DOF) of a Fresnel zone plate lens. Structural features of 3D-reconstructed eukaryotic cells that are affected by DOF artifacts in standard reconstruction are now recovered. This approach, based on focal series projections, is easily applicable with closed expressions to select specific data acquisition parameters.

Reconstruction from Microscopic Projections with Defocus-Gradient and Attenuation Effects

We discuss and illustrate defocus-gradient and attenuation effects that are part of the image formation models of microscopy of biological specimens. We demonstrate how they affect the projection data and in turn the 3D reconstructions. Biologically meaningful results can be obtained ignoring both of these effects, but using image processing techniques to incorporate corrections for them into reconstruction methods provides more accurate reconstructions, with potential for creating higher-resolution models of the biological specimens.

A Holistic Sequence of Programming Assignments for CS2 (Abstract Only)

We present a sequence of programming projects for the CS2 introductory computer science course which provides a holistic experience for students in preparation for their future roles in any workplace in which software is developed, whether in academia, government, industry, or elsewhere. The progression of projects has several key features: (1) they are easily reused simply by changing the underlying input data set; (2) they offer a flexible degree of analysis objectives; (3) they take advantage of freely available open source data sets and encourage their use; (4) they are designed to be small models of the kinds of problems likely to be encountered outside of the classroom environment; (5) they facilitate the introduction of increasingly more sophisticated software testing concepts, starting with the most elementary; (6) a student who attempts to do them in earnest, even if unsuccessful, can still learn important lessons about the different facets of programming and problem solving; and (7) a students understanding of the relationship between choice of data representation and performance will likely mature if he or she successfully completes the assignments. In our poster, we present the first and last assignments of the sequence that we have employed in a CS2 course, and discuss some results. We also show how these assignments can serve as a paradigm that may be used in other CS2-like courses. Many of the underlying concepts can also be applied to CS1-like courses as well as more advanced computer science courses.

Correction of distance-dependent blurring in projection data for fully three-dimensional electron microscopic reconstruction

We propose a method of correction for distance-dependent blurring, which is one of the limiting factors to achieving higher resolution in 3D reconstructions of biological specimens from 2D projections obtained by an electron microscope. Our proposed correction is based on the frequency-distance relation that has been used successfully in correction of a similar problem in single photon emission tomography and has been suggested for electron microscopy data obtained by rotating a sample around a single axis. We extend these approaches to electron microscopy data that are obtained from arbitrary directions. We develop the theoretical background for a correction method that results in an estimate of a true projection data set, which then can be used to obtain a 3D reconstruction by any currently existing algorithm.