Critical Parameter Values and Reconstruction Properties of Discrete Tomography: Application to Experimental Fluid Dynamics

We analyze representative ill-posed scenarios of tomographic PIV with a focus on conditions for unique volume reconstruction. Based on sparse random seedings of a region of interest with small particles, the corresponding systems of linear projection equations are probabilistically analyzed in order to determine (i) the ability of unique reconstruction in terms of the imaging geometry and the critical sparsity parameter, and (ii) sharpness of the transition to non-unique reconstruction with ghost particles when choosing the sparsity parameter improperly. The sparsity parameter directly relates to the seeding density used for PIV in experimental fluids dynamics that is chosen empirically to date. Our results provide a basic mathematical characterization of the PIV volume reconstruction problem that is an essential prerequisite for any algorithm used to actually compute the reconstruction. Moreover, we connect the sparse volume function reconstruction problem from few tomographic projections to major developments in compressed sensing.Comment: 22 pages, submitted to Fundamenta Informaticae. arXiv admin note: text overlap with arXiv:1208.589

Imaging and 3D reconstruction of membrane protein complexes by cryo-electron microscopy and single particle analysis

Cryo-electron microscopy (cryo-EM) in combination with single particle image processing and volume reconstruction is a powerful technology to obtain medium-resolution structures of large protein complexes, which are extremely difficult to crystallize and not amenable to NMR studies due to size limitation. Depending on the stability and stiffness as well as on the symmetry of the complex, three-dimensional reconstructions at a resolution of 10-30 ˚ can be achieved. In this range of resolution, we may not be able to answer A chemical questions at the level of atomic interactions, but we can gain detailed insight into the macromolecular architecture of large multi-subunit complexes and their mechanisms of action. In this thesis, several prevalently large membrane protein complexes of great physiological importance were examined by various electron microscopy techniques and single particle image analysis. The core part of my work consists in the imaging of a mammalian V-ATPase, frozen-hydrated in amorphous ice and of the completion of the first volume reconstruction of this type of enzyme, derived from cryo-EM images. This ubiquitous rotary motor is essential in every eukaryotic cell and is of high medical importance due to its implication in various diseases such as osteoporosis, skeletal cancer and kidney disorders. My contribution to the second and third paper concerns the volume reconstruction of two bacterial outer membrane pore complexes from cryo-EM images recorded by my colleague Mohamed Chami. PulD from Klebsiella oxytoca constitutes a massive translocating pore capable of transporting a fully folded cell surface protein PulA through the membrane. It is part of the Type II secretion system, which is common for Gram-negative bacteria. The second volume regards ClyA, a pore-forming heamolytic toxin of virulent Escherichia coli and Salmonella enterica strains that kill target cells by inserting pores into their membranes. To the last two papers, I contributed with cryo-negative stain imaging of the cell division protein DivIVA from Bacillus subtilis and with image processing of the micrographs displaying the siderophore receptor FrpB from Neisseria meningitidis

PVR: Patch-to-Volume Reconstruction for Large Area Motion Correction of Fetal MRI

In this paper we present a novel method for the correction of motion artifacts that are present in fetal Magnetic Resonance Imaging (MRI) scans of the whole uterus. Contrary to current slice-to-volume registration (SVR) methods, requiring an inflexible anatomical enclosure of a single investigated organ, the proposed patch-to-volume reconstruction (PVR) approach is able to reconstruct a large field of view of non-rigidly deforming structures. It relaxes rigid motion assumptions by introducing a specific amount of redundant information that is exploited with parallelized patch-wise optimization, super-resolution, and automatic outlier rejection. We further describe and provide an efficient parallel implementation of PVR allowing its execution within reasonable time on commercially available graphics processing units (GPU), enabling its use in the clinical practice. We evaluate PVR's computational overhead compared to standard methods and observe improved reconstruction accuracy in presence of affine motion artifacts of approximately 30% compared to conventional SVR in synthetic experiments. Furthermore, we have evaluated our method qualitatively and quantitatively on real fetal MRI data subject to maternal breathing and sudden fetal movements. We evaluate peak-signal-to-noise ratio (PSNR), structural similarity index (SSIM), and cross correlation (CC) with respect to the originally acquired data and provide a method for visual inspection of reconstruction uncertainty. With these experiments we demonstrate successful application of PVR motion compensation to the whole uterus, the human fetus, and the human placenta.Comment: 10 pages, 13 figures, submitted to IEEE Transactions on Medical Imaging. v2: wadded funders acknowledgements to preprin

Satellite-based auroral tomography and time-varying volume reconstruction

Tomography, originally developed to observe the internal structure of a human body in medical applications, can also be applied to research in Space Science applications. An upcoming satellite mission incorporates two imagers for auroral observation in the upper atmosphere. For this mission, development of auroral volume reconstruction using tomographic imaging is useful for understanding the internal structure of auroras. We have shown that beam-pixel clipping in image reconstruction improves the quality of reconstructed images, compared to previous techniques. The goal is to develop a suitable algorithm for auroral volume reconstruction using auroral images measured from satellite-borne optical instruments. We have demonstrated that weighting factor approximation in algebraic methods plays a crucial role in the quality of volume reconstruction. We also have evaluated the effectiveness of this algorithm with measured images of known volumes using perspective projections. In addition, a time-varying volume reconstruction scheme is discussed where auroras move over time

Efficient 3D Volume Reconstruction from a Point Cloud Using a Phase-Field Method

We propose an explicit hybrid numerical method for the efficient 3D volume reconstruction from unorganized point clouds using a phase-field method. The proposed three-dimensional volume reconstruction algorithm is based on the 3D binary image segmentation method. First, we define a narrow band domain embedding the unorganized point cloud and an edge indicating function. Second, we define a good initial phase-field function which speeds up the computation significantly. Third, we use a recently developed explicit hybrid numerical method for solving the three-dimensional image segmentation model to obtain efficient volume reconstruction from point cloud data. In order to demonstrate the practical applicability of the proposed method, we perform various numerical experiments