Easy implementation of advanced tomography algorithms using the ASTRA toolbox with Spot operators

Mathematical scripting languages are commonly used to develop new tomographic reconstruction algorithms. For large experimental datasets, high performance parallel (GPU) implementations are essential, requiring a re-implementation of the algorithm using a language that is closer to the computing hardware. In this paper, we introduce a new Matlab interface to the ASTRA toolbox, a high performance toolbox for building tomographic reconstruction algorithms. By exposing the ASTRA linear tomography operators through a standard Matlab matrix syntax, existing and new reconstruction algorithms implemented in Matlab can now be applied directly to large experimental datasets. This is achieved by using the Spot toolbox, which wraps external code for linear operations into Matlab objects that can be used as matrices. We provide a series of examples that demonstrate how this Spot operator can be used in combination with existing algorithms implemented in Matlab and how it can be used for rapid development of new algorithms, resulting in direct applicability to large-scale experimental datasets

The ASTRA Toolbox: A platform for advanced algorithm development in electron tomography

We present the ASTRA Toolbox as an open platform for 3D image reconstruction in tomography. Most of the software tools that are currently used in electron tomography offer limited flexibility with respect to the geometrical parameters of the acquisition model and the algorithms used for reconstruction. The ASTRA Toolbox provides an extensive set of fast and flexible building blocks that can be used to develop advanced reconstruction algorithms, effectively removing these limitations. We demonstrate this flexibility, the resulting reconstruction quality, and the computational efficiency of this toolbox by a series of experiments, based on experimental dual-axis tilt series

Fixing Nonconvergence of Algebraic Iterative Reconstruction with an Unmatched Backprojector

We consider algebraic iterative reconstruction methods with applications in image reconstruction. In particular, we are concerned with methods based on an unmatched projector/backprojector pair; i.e., the backprojector is not the exact adjoint or transpose of the forward projector. Such situations are common in large-scale computed tomography, and we consider the common situation where the method does not converge due to the nonsymmetry of the iteration matrix. We propose a modified algorithm that incorporates a small shift parameter, and we give the conditions that guarantee convergence of this method to a fixed point of a slightly perturbed problem. We also give perturbation bounds for this fixed point. Moreover, we discuss how to use Krylov subspace methods to efficiently estimate the leftmost eigenvalue of a certain matrix to select a proper shift parameter. The modified algorithm is illustrated with test problems from computed tomography

Iterative and discrete reconstruction in the evaluation of the rabbit model of osteoarthritis

Micro-computed tomography (µCT) is a standard method for bone morphometric evaluation. However, the scan time can be long and the radiation dose during the scan may have adverse effects on test subjects, therefore both of them should be minimized. This could be achieved by applying iterative reconstruction (IR) on sparse projection data, as IR is capable of producing reconstructions of sufficient image quality with less projection data than the traditional algorithm requires. In this work, the performance of three IR algorithms was assessed for quantitative bone imaging from low-resolution data in the evaluation of the rabbit model of osteoarthritis. Subchondral bone images were reconstructed with a conjugate gradient least squares algorithm, a total variation regularization scheme, and a discrete algebraic reconstruction technique to obtain quantitative bone morphometry, and the results obtained in this manner were compared with those obtained from the reference reconstruction. Our approaches were sufficient to identify changes in bone structure in early osteoarthritis, and these changes were preserved even when minimal data were provided for the reconstruction. Thus, our results suggest that IR algorithms give reliable performance with sparse projection data, thereby recommending them for use in µCT studies where time and radiation exposure are preferably minimized. © 2018, The Author(s).Peer reviewe

Tomosipo: fast, flexible, and convenient 3D tomography for complex scanning geometries in Python

Tomography is a powerful tool for reconstructing the interior of an object from a series of projection images. Typically, the source and detector traverse a standard path (e.g., circular, helical). Recently, various techniques have emerged that use more complex acquisition geometries. Current software packages require significant handwork, or lack the flexibility to handle such geometries. Therefore, software is needed that can concisely represent, visualize, and compute reconstructions of complex acquisition geometries. We present tomosipo, a Python package that provides these capabilities in a concise and intuitive way. Case studies demonstrate the power and flexibility of tomosipo

Three dimensional mapping of Fe dopants in ceria nanocrystals using direct spectroscopic electron tomography

Electron tomography is a powerful technique for the 3D characterization of the morphology of nanostructures. Nevertheless, resolving the chemical composition of complex nanostructures in 3D remains challenging and the number of studies in which electron energy loss spectroscopy (EELS) is combined with tomography is limited. During the last decade, dedicated reconstruction algorithms have been developed for HAADF-STEM tomography using prior knowledge about the investigated sample. Here, we will use the prior knowledge that the experimental spectrum of each reconstructed voxel is a linear combination of a well-known set of references spectra in a so-called direct spectroscopic tomography technique. Based on a simulation experiment, it is shown that this technique provides superior results in comparison to conventional reconstruction methods for spectroscopic data, especially for spectrum images containing a relatively low signal to noise ratio. Next, this technique is used to investigate the spatial distribution of Fe dopants in Fe:Ceria nanoparticles in 3D. It is shown that the presence of the Fe2+ dopants is correlated with a reduction of the Ce atoms from Ce4+ towards Ce3+. In addition, it is demonstrated that most of the Fe dopants are located near the voids inside the nanoparticle

A parametric level-set method for partially discrete tomography

This paper introduces a parametric level-set method for tomographic reconstruction of partially discrete images. Such images consist of a continuously varying background and an anomaly with a constant (known) grey-value. We represent the geometry of the anomaly using a level-set function, which we represent using radial basis functions. We pose the reconstruction problem as a bi-level optimization problem in terms of the background and coefficients for the level-set function. To constrain the background reconstruction we impose smoothness through Tikhonov regularization. The bi-level optimization problem is solved in an alternating fashion; in each iteration we first reconstruct the background and consequently update the level-set function. We test our method on numerical phantoms and show that we can successfully reconstruct the geometry of the anomaly, even from limited data. On these phantoms, our method outperforms Total Variation reconstruction, DART and P-DART.Comment: Paper submitted to 20th International Conference on Discrete Geometry for Computer Imager

Convolutional Dictionary Regularizers for Tomographic Inversion

There has been a growing interest in the use of data-driven regularizers to solve inverse problems associated with computational imaging systems. The convolutional sparse representation model has recently gained attention, driven by the development of fast algorithms for solving the dictionary learning and sparse coding problems for sufficiently large images and data sets. Nevertheless, this model has seen very limited application to tomographic reconstruction problems. In this paper, we present a model-based tomographic reconstruction algorithm using a learnt convolutional dictionary as a regularizer. The key contribution is the use of a data-dependent weighting scheme for the l1 regularization to construct an effective denoising method that is integrated into the inversion using the Plug-and-Play reconstruction framework. Using simulated data sets we demonstrate that our approach can improve performance over traditional regularizers based on a Markov random field model and a patch-based sparse representation model for sparse and limited-view tomographic data sets