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

BioEM: GPU-accelerated computing of Bayesian inference of electron microscopy images

In cryo-electron microscopy (EM), molecular structures are determined from large numbers of projection images of individual particles. To harness the full power of this single-molecule information, we use the Bayesian inference of EM (BioEM) formalism. By ranking structural models using posterior probabilities calculated for individual images, BioEM in principle addresses the challenge of working with highly dynamic or heterogeneous systems not easily handled in traditional EM reconstruction. However, the calculation of these posteriors for large numbers of particles and models is computationally demanding. Here we present highly parallelized, GPU-accelerated computer software that performs this task efficiently. Our flexible formulation employs CUDA, OpenMP, and MPI parallelization combined with both CPU and GPU computing. The resulting BioEM software scales nearly ideally both on pure CPU and on CPU+GPU architectures, thus enabling Bayesian analysis of tens of thousands of images in a reasonable time. The general mathematical framework and robust algorithms are not limited to cryo-electron microscopy but can be generalized for electron tomography and other imaging experiments

A Streaming Multi-GPU Implementation of Image Simulation Algorithms for Scanning Transmission Electron Microscopy

Simulation of atomic resolution image formation in scanning transmission electron microscopy can require significant computation times using traditional methods. A recently developed method, termed plane-wave reciprocal-space interpolated scattering matrix (PRISM), demonstrates potential for significant acceleration of such simulations with negligible loss of accuracy. Here we present a software package called Prismatic for parallelized simulation of image formation in scanning transmission electron microscopy (STEM) using both the PRISM and multislice methods. By distributing the workload between multiple CUDA-enabled GPUs and multicore processors, accelerations as high as 1000x for PRISM and 30x for multislice are achieved relative to traditional multislice implementations using a single 4-GPU machine. We demonstrate a potentially important application of Prismatic, using it to compute images for atomic electron tomography at sufficient speeds to include in the reconstruction pipeline. Prismatic is freely available both as an open-source CUDA/C++ package with a graphical user interface and as a Python package, PyPrismatic

Blur resolved OCT: full-range interferometric synthetic aperture microscopy through dispersion encoding

We present a computational method for full-range interferometric synthetic aperture microscopy (ISAM) under dispersion encoding. With this, one can effectively double the depth range of optical coherence tomography (OCT), whilst dramatically enhancing the spatial resolution away from the focal plane. To this end, we propose a model-based iterative reconstruction (MBIR) method, where ISAM is directly considered in an optimization approach, and we make the discovery that sparsity promoting regularization effectively recovers the full-range signal. Within this work, we adopt an optimal nonuniform discrete fast Fourier transform (NUFFT) implementation of ISAM, which is both fast and numerically stable throughout iterations. We validate our method with several complex samples, scanned with a commercial SD-OCT system with no hardware modification. With this, we both demonstrate full-range ISAM imaging, and significantly outperform combinations of existing methods.Comment: 17 pages, 7 figures. The images have been compressed for arxiv - please follow DOI for full resolutio

Deep D-Bar: Real-Time Electrical Impedance Tomography Imaging With Deep Neural Networks

The mathematical problem for electrical impedance tomography (EIT) is a highly nonlinear ill-posed inverse problem requiring carefully designed reconstruction procedures to ensure reliable image generation. D-bar methods are based on a rigorous mathematical analysis and provide robust direct reconstructions by using a low-pass filtering of the associated nonlinear Fourier data. Similarly to low-pass filtering of linear Fourier data, only using low frequencies in the image recovery process results in blurred images lacking sharp features, such as clear organ boundaries. Convolutional neural networks provide a powerful framework for post-processing such convolved direct reconstructions. In this paper, we demonstrate that these CNN techniques lead to sharp and reliable reconstructions even for the highly nonlinear inverse problem of EIT. The network is trained on data sets of simulated examples and then applied to experimental data without the need to perform an additional transfer training. Results for absolute EIT images are presented using experimental EIT data from the ACT4 and KIT4 EIT systems

TomocuPy: efficient GPU-based tomographic reconstruction with asynchronous data processing

Fast 3D data analysis and steering of a tomographic experiment by changing environmental conditions or acquisition parameters require fast, close to real-time, 3D reconstruction of large data volumes. Here we present a performance-optimized TomocuPy package as a GPU alternative to the commonly-used CPU-based TomoPy package for tomographic reconstruction. TomocuPy utilizes modern hardware capabilities to organize a 3D asynchronous reconstruction involving parallel read-write operations with storage drives, CPU-GPU data transfers, and GPU computations. In the asynchronous reconstruction, all the operations are timely overlapped to almost fully hide all data management time. Since most cameras work with less than 16-bit digital output, we furthermore optimize the memory usage and processing speed by using 16-bit floating-point arithmetic. As a result, 3D reconstruction with TomocuPy became 20-30 times faster than its multithreaded CPU equivalent. Full reconstruction (including read-write operations and methods initialization) of a 2048x2048x2048 tomographic volume takes less than 7~s on a single Nvidia Tesla A100 and PCIe 4.0 NVMe SSD, and scales almost linearly increasing the data size. To simplify operation at synchrotron beamlines, TomocuPy provides an easy-to-use command-line interface. Efficacy of the package was demonstrated during a tomographic experiment on gas-hydrate formation in porous samples, where a steering option was implemented as a lens-changing mechanism for zooming to regions of interest

Phase-Retrieved Tomography enables imaging of a Tumor Spheroid in Mesoscopy Regime

Optical tomographic imaging of biological specimen bases its reliability on the combination of both accurate experimental measures and advanced computational techniques. In general, due to high scattering and absorption in most of the tissues, multi view geometries are required to reduce diffuse halo and blurring in the reconstructions. Scanning processes are used to acquire the data but they inevitably introduces perturbation, negating the assumption of aligned measures. Here we propose an innovative, registration free, imaging protocol implemented to image a human tumor spheroid at mesoscopic regime. The technique relies on the calculation of autocorrelation sinogram and object autocorrelation, finalizing the tomographic reconstruction via a three dimensional Gerchberg Saxton algorithm that retrieves the missing phase information. Our method is conceptually simple and focuses on single image acquisition, regardless of the specimen position in the camera plane. We demonstrate increased deep resolution abilities, not achievable with the current approaches, rendering the data alignment process obsolete.Comment: 21 pages, 5 figure