Enhanced hyperspectral tomography for bioimaging by spatiospectral reconstruction.

Here we apply hyperspectral bright field imaging to collect computed tomographic images with excellent energy resolution (~ 1 keV), applying it for the first time to map the distribution of stain in a fixed biological sample through its characteristic K-edge. Conventionally, because the photons detected at each pixel are distributed across as many as 200 energy channels, energy-selective images are characterised by low count-rates and poor signal-to-noise ratio. This means high X-ray exposures, long scan times and high doses are required to image unique spectral markers. Here, we achieve high quality energy-dispersive tomograms from low dose, noisy datasets using a dedicated iterative reconstruction algorithm. This exploits the spatial smoothness and inter-channel structural correlation in the spectral domain using two carefully chosen regularisation terms. For a multi-phase phantom, a reduction in scan time of 36 times is demonstrated. Spectral analysis methods including K-edge subtraction and absorption step-size fitting are evaluated for an ex vivo, single (iodine)-stained biological sample, where low chemical concentration and inhomogeneous distribution can affect soft tissue segmentation and visualisation. The reconstruction algorithms are available through the open-source Core Imaging Library. Taken together, these tools offer new capabilities for visualisation and elemental mapping, with promising applications for multiply-stained biological specimens.

Core Imaging Library - Part II: multichannel reconstruction for dynamic and spectral tomography.

The newly developed core imaging library (CIL) is a flexible plug and play library for tomographic imaging with a specific focus on iterative reconstruction. CIL provides building blocks for tailored regularized reconstruction algorithms and explicitly supports multichannel tomographic data. In the first part of this two-part publication, we introduced the fundamentals of CIL. This paper focuses on applications of CIL for multichannel data, e.g. dynamic and spectral. We formalize different optimization problems for colour processing, dynamic and hyperspectral tomography and demonstrate CIL's capabilities for designing state-of-the-art reconstruction methods through case studies and code snapshots. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 2'.

New software protocols for enabling laboratory based temporal CT.

Temporal micro-computed tomography (CT) allows the non-destructive quantification of processes that are evolving over time in 3D. Despite the increasing popularity of temporal CT, the practical implementation and optimisation can be difficult. Here, we present new software protocols that enable temporal CT using commercial laboratory CT systems. The first protocol drastically reduces the need for periodic intervention when making time-lapse experiments, allowing a large number of tomograms to be collected automatically. The automated scanning at regular intervals needed for uninterrupted time-lapse CT is demonstrated by analysing the germination of a mung bean (vigna radiata), whilst the synchronisation with an in situ rig required for interrupted time-lapse CT is highlighted using a shear cell to observe granular segregation. The second protocol uses golden-ratio angular sampling with an iterative reconstruction scheme and allows the number of projections in a reconstruction to be changed as sample evolution occurs. This overcomes the limitation of the need to know a priori what the best time window for each scan is. The protocol is evaluated by studying barite precipitation within a porous column, allowing a comparison of spatial and temporal resolution of reconstructions with different numbers of projections. Both of the protocols presented here have great potential for wider application, including, but not limited to, in situ mechanical testing, following battery degradation and chemical reactions.

EMPIRICAL AVERAGE-CASE RELATION BETWEEN UNDERSAMPLING AND SPARSITY IN X-RAY CT.

In X-ray computed tomography (CT) it is generally acknowledged that reconstruction methods exploiting image sparsity allow reconstruction from a significantly reduced number of projections. The use of such reconstruction methods is inspired by recent progress in compressed sensing (CS). However, the CS framework provides neither guarantees of accurate CT reconstruction, nor any relation between sparsity and a sufficient number of measurements for recovery, i.e., perfect reconstruction from noise-free data. We consider reconstruction through 1-norm minimization, as proposed in CS, from data obtained using a standard CT fan-beam sampling pattern. In empirical simulation studies we establish quantitatively a relation between the image sparsity and the sufficient number of measurements for recovery within image classes motivated by tomographic applications. We show empirically that the specific relation depends on the image class and in many cases exhibits a sharp phase transition as seen in CS, i.e., same-sparsity images require the same number of projections for recovery. Finally we demonstrate that the relation holds independently of image size and is robust to small amounts of additive Gaussian white noise.

Few-view single photon emission computed tomography (SPECT) reconstruction based on a blurred piecewise constant object model.

A sparsity-exploiting algorithm intended for few-view single photon emission computed tomography (SPECT) reconstruction is proposed and characterized. The algorithm models the object as piecewise constant subject to a blurring operation. To validate that the algorithm closely approximates the true object in the noiseless case, projection data were generated from an object assuming this model and using the system matrix. Monte Carlo simulations were performed to provide more realistic data of a phantom with varying smoothness across the field of view and a cardiac phantom. Reconstructions were performed across a sweep of two primary design parameters. The results demonstrate that the algorithm recovers the object in a noiseless simulation case. While the algorithm assumes a specific blurring model, the results suggest that the algorithm may provide high reconstruction accuracy even when the object does not match the assumed blurring model. Generally, increased values of the blurring parameter and total variation weighting parameters reduced streaking artifacts, while decreasing spatial resolution. The proposed algorithm demonstrated higher correlation with respect to the true phantom compared to maximum-likelihood expectation maximization (MLEM) reconstructions. Images reconstructed with the proposed algorithm demonstrated reduced streaking artifacts when reconstructing from few views compared to MLEM. The proposed algorithm introduced patchy artifacts in some reconstructed images, depending on the noise level and the selected algorithm parameters. Overall, the results demonstrate preliminary feasibility of a sparsity-exploiting reconstruction algorithm which may be beneficial for few-view SPECT.

First-order convex feasibility algorithms for x-ray CT.

PURPOSE: Iterative image reconstruction (IIR) algorithms in computed tomography (CT) are based on algorithms for solving a particular optimization problem. Design of the IIR algorithm, therefore, is aided by knowledge of the solution to the optimization problem on which it is based. Often times, however, it is impractical to achieve accurate solution to the optimization of interest, which complicates design of IIR algorithms. This issue is particularly acute for CT with a limited angular-range scan, which leads to poorly conditioned system matrices and difficult to solve optimization problems. In this paper, we develop IIR algorithms which solve a certain type of optimization called convex feasibility. The convex feasibility approach can provide alternatives to unconstrained optimization approaches and at the same time allow for rapidly convergent algorithms for their solution-thereby facilitating the IIR algorithm design process. METHODS: An accelerated version of the Chambolle-Pock (CP) algorithm is adapted to various convex feasibility problems of potential interest to IIR in CT. One of the proposed problems is seen to be equivalent to least-squares minimization, and two other problems provide alternatives to penalized, least-squares minimization. RESULTS: The accelerated CP algorithms are demonstrated on a simulation of circular fan-beam CT with a limited scanning arc of 144°. The CP algorithms are seen in the empirical results to converge to the solution of their respective convex feasibility problems. CONCLUSIONS: Formulation of convex feasibility problems can provide a useful alternative to unconstrained optimization when designing IIR algorithms for CT. The approach is amenable to recent methods for accelerating first-order algorithms which may be particularly useful for CT with limited angular-range scanning. The present paper demonstrates the methodology, and future work will illustrate its utility in actual CT application.

Quantifying admissible undersampling for sparsity-exploiting iterative image reconstruction in X-ray CT.

Iterative image reconstruction with sparsity-exploiting methods, such as total variation (TV) minimization, investigated in compressive sensing claim potentially large reductions in sampling requirements. Quantifying this claim for computed tomography (CT) is nontrivial, because both full sampling in the discrete-to-discrete imaging model and the reduction in sampling admitted by sparsity-exploiting methods are ill-defined. The present article proposes definitions of full sampling by introducing four sufficient-sampling conditions (SSCs). The SSCs are based on the condition number of the system matrix of a linear imaging model and address invertibility and stability. In the example application of breast CT, the SSCs are used as reference points of full sampling for quantifying the undersampling admitted by reconstruction through TV-minimization. In numerical simulations, factors affecting admissible undersampling are studied. Differences between few-view and few-detector bin reconstruction as well as a relation between object sparsity and admitted undersampling are quantified.