An efficient quasi-Monte Carlo method with forced fixed detection for photon scatter simulation in CT.

Detected scattered photons can cause cupping and streak artifacts, significantly degrading the quality of CT images. For fast and accurate estimation of scatter intensities resulting from photon interactions with a phantom, we first transform the path probability of photons interacting with the phantom into a high-dimensional integral. Secondly, we develope a new efficient algorithm called gQMCFFD, which combines graphics processing unit(GPU)-based quasi-Monte Carlo (QMC) with forced fixed detection to approximate this integral. QMC uses low discrepancy sequences for simulation and is deterministic versions of Monte Carlo. Numerical experiments show that the results are in excellent agreement and the efficiency improvement factors are 4 ∼ 46 times in all simulations by gQMCFFD with comparison to GPU-based Monte Carlo methods. And by combining gQMCFFD with sparse matrix method, the simulation time is reduced to 2 seconds in a single projection angle and the relative difference is 3.53%.

One-Step Method for Material Quantitation Using In-Line Tomography With Single Scanning.

OBJECTIVE: Quantitative technique based on In-line phase-contrast computed tomography with single scanning attracts more attention in application due to the flexibility of the implementation. However, the quantitative results usually suffer from artifacts and noise since the phase retrieval and reconstruction are independent ("two-step") without feedback from the original data. The work aims to investigate a method for material quantitation to improve the image quality of In-line tomography within single scanning. METHOD: An iterative method based Fresnel diffraction imaging model is developed in this work, which directly reconstructs the refractive index decrement δ and imaginary ß of the object from observed data ("one-step"). Moreover, high-quality material decomposition results are obtained by using a linear approximation in the iterative process. RESULTS: Compared with the existing methods, Our method shows a higher peak signal-to-noise ratio and structural similarity in numerical experimental results. Additionally, the quantitation accuracy of the proposed method is greater than 97.2 % by calculating the equivalent atomic number of the decomposed basic material in the real experiment. CONCLUSION: We demonstrate that this one-step method greatly reduces noise and improves quantitative reconstruction and decomposition results. SIGNIFICANCE: This algorithm has the potential for quantitative imaging research using In-line tomography in future biomedical applications.

Quasi-Monte Carlo method for calculating X-ray scatter in CT.

In this paper we transform the trajectories of X-ray as it interacts with a phantom into a high-dimensional integration problem and give the integral formula for the probability of photons emitted from the X-ray source through the phantom to reach the detector. We propose a superior algorithm called gQMCFRD, which combines GPU-based quasi-Monte Carlo (gQMC) method with forced random detection (FRD) technique to simulate this integral. QMC simulation is deterministic versions of Monte Carlo (MC) simulation, which uses deterministic low discrepancy points (such as Sobol' points) instead of the random points. By using the QMC and FRD technique, the gQMCFRD greatly increases the simulation convergence rate and efficiency. We benchmark gQMCFRD, GPU based MC tool (gMCDRR), which performs conventional simulations, a GPU-based Metropolis MC tool (gMMC), which uses the Metropolis-Hasting algorithm to sample the entire photon path from the X-ray source to the detector and gMCFRD, that uses random points for sampling against PENELOPE subroutines: MC-GPU. The results are in excellent agreement and the Efficiency Improvement Factor range 27 ∼ 37 (or 1.09 ∼ 1.16, or 0.12 ∼ 0.15, or 3.62 ∼ 3.70) by gQMCFRD (or gMCDRR, or gMMC, or gMCFRD) with comparison to MC-GPU in all cases. It shows that gQMCFRD is more effective in these cases.

A method for material decomposition and quantification with grating based phase CT.

Material decomposition (MD) is an important application of computer tomography (CT). For phase contrast imaging, conventional MD methods are categorized into two types with respect to different operation sequences, i.e., "before" or "after" image reconstruction. Both categories come down to two-step methods, which have the problem of noise amplification. In this study, we incorporate both phase and absorption (PA) information into MD process, and correspondingly develop a simultaneous algebraic reconstruction technique (SART). The proposed method is referred to as phase & absorption material decomposition-SART (PAMD-SART). By iteratively solving an optimization problem, material composition and substance quantification are reconstructed directly from absorption and differential phase projections. Comparing with two-step MD, the proposed one-step method is superior in noise suppression and accurate decomposition. Numerical simulations and synchrotron radiation based experiments show that PAMD-SART outperforms the classical MD method (image-based and dual-energy CT iterative method), especially for the quantitative accuracy of material equivalent atomic number.

Locally linear transform based three-dimensional gradient L 0 -norm minimization for spectral CT reconstruction.

PURPOSE: Spectral computed tomography (CT) is proposed by extending the conventional CT along the energy dimension. One newly implementation is to employ an energy-discriminating photon counting detector (PCD), which can distinguish photon energy and divide a whole x-ray spectrum into several energy bins with appropriate post-processing steps. The state-of-the-art PCD-based spectral CT has superior energy resolution and material distinguishability, and it further has a great potential in both medical and industrial applications. To improve the reconstruction quality and decomposition accuracy, in this work, we propose an optimization-based spectral CT reconstruction method with an innovational sparsity constraint. METHODS: We first employ a locally linear transform to the reconstructed channel images, and the structural similarity along the spectral dimension is effectively converted to a one-dimensional (1D) gradient sparsity. Then, combining the prior knowledge of piecewise constant in the spatial domain (e.g., a two-dimensional (2D) gradient sparsity feature), we unify both spectral and spatial dimensions and establish a joint three-dimensional (3D) gradient sparsity. In addition, we use the L 0 -norm to measure the proposed sparsity and incorporate it as a smoothness constraint to concretize a general optimization framework. Furthermore, we develop the corresponding iterative algorithm to solve the optimization problem. RESULTS: Both visual results and quantitative indexes of numerical simulations and phantom experiments demonstrate the proposed method outperform the conventional filtered backprojection (FBP), total variation (TV), 2D L0 -norm (L0 ), and TV with low rank (TVLR)-based methods. From the image and ROI comparisons, we find the proposed method performs well in noise suppression, detail maintenance, and decomposition accuracy. However, the FBP suffers severe noise, the TV and L0 are difficult to work consistently among different energy bins, and the TVLR fails to avoid gray value shift. The image quality assessments, such as peak signal-to-noise ratio (PSNR), normal mean absolute deviation (NMAD). and structural similarity (SSIM), also consistently indicate the proposed method can effectively removing noise and keeping fine structures in both channel-wise reconstructions and material decompositions. CONCLUSIONS: By employing a locally linear transform, the structural similarity among spectral channel images is converted to a 1D gradient sparsity and the gray value shift is effectively avoided when the difference measurement is minimized. The 3D L0 -norm jointly and uniformly measures the gradient sparsity in both spectral and spatial dimensions. The cooperation of locally linear transform and 3D L0 -norm well reinforces the global sparse features and keeps the correlation along spectral dimension without bringing gray-value distortions. The corresponding constraint optimization model is fast and stably solved by using an alternative direction technique. Both numerical simulations and phantom experiments confirm the superior performance of the proposed method in noise suppression, structure maintenance, and accurate decomposition.

Dual phase grating based X-ray differential phase contrast imaging with source grating: theory and validation.

In this work, we developed a new theoretical framework using wave optics to explain the working mechanism of the grating based X-ray differential phase contrast imaging (XPCI) interferometer systems consist of more than one phase grating. Under the optical reversibility principle, the wave optics interpretation was simplified into the geometrical optics interpretation, in which the phase grating was treated as a thin lens. Moreover, it was derived that the period of an arrayed source, e.g., the period of a source grating, is always equal to the period of the diffraction fringe formed on the source plane. When a source grating is utilized, the theory indicated that it is better to keep the periods of the two phase gratings different to generate large period diffraction fringes. Experiments were performed to validate these theoretical findings.

Spectrum Estimation-Guided Iterative Reconstruction Algorithm for Dual Energy CT.

X-ray spectrum plays a very important role in dual energy computed tomography (DECT) reconstruction. Because it is difficult to measure x-ray spectrum directly in practice, efforts have been devoted into spectrum estimation by using transmission measurements. These measurement methods are independent of the image reconstruction, which bring extra cost and are time consuming. Furthermore, the estimated spectrum mismatch would degrade the quality of the reconstructed images. In this paper, we propose a spectrum estimation-guided iterative reconstruction algorithm for DECT which aims to simultaneously recover the spectrum and reconstruct the image. The proposed algorithm is formulated as an optimization framework combining spectrum estimation based on model spectra representation, image reconstruction, and regularization for noise suppression. To resolve the multi-variable optimization problem of simultaneously obtaining the spectra and images, we introduce the block coordinate descent (BCD) method into the optimization iteration. Both the numerical simulations and physical phantom experiments are performed to verify and evaluate the proposed method. The experimental results validate the accuracy of the estimated spectra and reconstructed images under different noise levels. The proposed method obtains a better image quality compared with the reconstructed images from the known exact spectra and is robust in noisy data applications.

The earliest Timematids in Burmese amber reveal diverse tarsal pads of stick insects in the mid-Cretaceous.

Many extant insects have developed pad structures, euplantulae or arolia on their tarsi to increase friction or enhance adhesion for better mobility. Many polyneopteran insects with euplantulae, for example, Grylloblattodea, Mantophasmatodea and Orthoptera, have been described from the Mesozoic. However, the origin and evolution of stick insects' euplantulae are poorly understood due to rare fossil records. Here, we report the earliest fossil records of Timematodea hitherto, Tumefactipes prolongates gen. et sp. nov. and Granosicorpes lirates gen. et sp. nov., based on three specimens from mid-Cretaceous Burmese amber. Specimens of Tumefactipes prolongates gen. et sp. nov. have extremely specialized and expanded euplantulae on their tarsomere II. These new findings are the first known and the earliest fossil records about euplantula structure within Phasmatodea, demonstrating the diversity of euplantulae in Polyneoptera during the Mesozoic. Such tarsal pads might have increased friction and helped these mid-Cretaceous stick insects to climb more firmly on various surfaces, such as broad leaves, wetted tree branches or ground. These specimens provide more morphological data for us to understand the relationships of Timematodea, Euphasmatodea, Orthoptera and Embioptera, suggesting that Timematodea might be monophyletic with Euphasmatodea rather than Embioptera and Phasmatodea should have a closer relationship with Orthoptera rather than Embioptera.