Expansion-maximization-compression algorithm with spherical harmonics for single particle imaging with X-ray lasers

In 3D single particle imaging with X-ray free-electron lasers, particle orientation is not recorded during measurement but is instead recovered as a necessary step in the reconstruction of a 3D image from the diffraction data. Here we use harmonic analysis on the sphere to cleanly separate the angu- lar and radial degrees of freedom of this problem, providing new opportunities to efficiently use data and computational resources. We develop the Expansion-Maximization-Compression algorithm into a shell-by-shell approach and implement an angular bandwidth limit that can be gradually raised during the reconstruction. We study the minimum number of patterns and minimum rotation sampling required for a desired angular and radial resolution. These extensions provide new av- enues to improve computational efficiency and speed of convergence, which are critically important considering the very large datasets expected from experiment

Fast algorithms and efficient GPU implementations for the Radon transform and the back-projection operator represented as convolution operators

The Radon transform and its adjoint, the back-projection operator, can both be expressed as convolutions in log-polar coordinates. Hence, fast algorithms for the application of the operators can be constructed by using FFT, if data is resampled at log-polar coordinates. Radon data is typically measured on an equally spaced grid in polar coordinates, and reconstructions are represented (as images) in Cartesian coordinates. Therefore, in addition to FFT, several steps of interpolation have to be conducted in order to apply the Radon transform and the back-projection operator by means of convolutions. Both the interpolation and the FFT operations can be efficiently implemented on Graphical Processor Units (GPUs). For the interpolation, it is possible to make use of the fact that linear interpolation is hard-wired on GPUs, meaning that it has the same computational cost as direct memory access. Cubic order interpolation schemes can be constructed by combining linear interpolation steps which provides important computation speedup. We provide details about how the Radon transform and the back-projection can be implemented efficiently as convolution operators on GPUs. For large data sizes, speedups of about 10 times are obtained in relation to the computational times of other software packages based on GPU implementations of the Radon transform and the back-projection operator. Moreover, speedups of more than a 1000 times are obtained against the CPU-implementations provided in the MATLAB image processing toolbox

Algebraic filter approach for fast approximation of nonlinear tomographic reconstruction methods

We present a computational approach for fast approximation of nonlinear tomographic reconstruction methods by filtered backprojection (FBP) methods. Algebraic reconstruction algorithms are the methods of choice in a wide range of tomographic applications, yet they require significant computation time, restricting their usefulness. We build upon recent work on the approximation of linear algebraic reconstruction methods and extend the approach to the approximation of nonlinear reconstruction methods which are common in practice. We demonstrate that if a blueprint image is available that is sufficiently similar to the scanned object, our approach can compute reconstructions that approximate iterative nonlinear methods, yet have the same speed as FBP

Deep Learning for Vanishing Point Detection Using an Inverse Gnomonic Projection

We present a novel approach for vanishing point detection from uncalibrated monocular images. In contrast to state-of-the-art, we make no a priori assumptions about the observed scene. Our method is based on a convolutional neural network (CNN) which does not use natural images, but a Gaussian sphere representation arising from an inverse gnomonic projection of lines detected in an image. This allows us to rely on synthetic data for training, eliminating the need for labelled images. Our method achieves competitive performance on three horizon estimation benchmark datasets. We further highlight some additional use cases for which our vanishing point detection algorithm can be used.Comment: Accepted for publication at German Conference on Pattern Recognition (GCPR) 2017. This research was supported by German Research Foundation DFG within Priority Research Programme 1894 "Volunteered Geographic Information: Interpretation, Visualisation and Social Computing

A Deep Belief Network and Case Reasoning Based Decision Model for Emergency Rescue

The frequent occurrence of major public emergencies in China has caused significant human and economic losses. To carry out successful rescue operations in such emergencies, decisions need to be made as efficiently as possible. Using earthquakes as an example of a public emergency, this paper combines the Deep Belief Network (DBN) and Case-Based Reasoning (CBR) models to improve the case representation and case retrieval steps in the decision-making process, then designs and constructs a decision-making model. The validity of the model is then verified by an example. The results of this study can be applied to maximize the efficiency of emergency rescue decisions