X-ray tomography: the way from layer-by-layer radiography to computed tomography

The methods of X-ray computed tomography allow us to study the internal morphological structure of objects in a non-destructive way. The evolution of these methods is similar in many respects to the evolution of photography, where complex optics were replaced by mobile phone cameras, and the computers built into the phone took over the functions of high-quality image generation. X-ray tomography originated as a method of hardware non-invasive imaging of a certain internal cross-section of the human body. Today, thanks to the advanced reconstruction algorithms, a method makes it possible to reconstruct a digital 3D image of an object with a submicron resolution. In this article, we will analyze the tasks that the software part of the tomographic complex has to solve in addition to managing the process of data collection. The issues that are still considered open are also discussed. The relationship between the spatial resolution of the method, sensitivity and the radiation load is reviewed. An innovative approach to the organization of tomographic imaging, called “reconstruction with monitoring”, is described. This approach makes it possible to reduce the radiation load on the object by at least 2 – 3 times. In this work, we show that when X-ray computed tomography moves towards increasing the spatial resolution and reducing the radiation load, the software part of the method becomes increasingly important.This work was supported by Russian Foundation for Basic Research (Projects No.18-29-26033, 18-29-26020)

Neural network regularization in the problem of few-view computed tomography

The computed tomography allows to reconstruct the inner morphological structure of an object without physical destructing. The accuracy of digital image reconstruction directly depends on the measurement conditions of tomographic projections, in particular, on the number of recorded projections. In medicine, to reduce the dose of the patient load there try to reduce the number of measured projections. However, in a few-view computed tomography, when we have a small number of projections, using standard reconstruction algorithms leads to the reconstructed images degradation. The main feature of our approach for few-view tomography is that algebraic reconstruction is being finalized by a neural network with keeping measured projection data because the additive result is in zero space of the forward projection operator. The final reconstruction presents the sum of the additive calculated with the neural network and the algebraic reconstruction. First is an element of zero space of the forward projection operator. The second is an element of orthogonal addition to the zero space. Last is the result of applying the algebraic reconstruction method to a few-angle sinogram. The dependency model between elements of zero space of forward projection operator and algebraic reconstruction is built with neural networks. It demonstrated that realization of the suggested approach allows achieving better reconstruction accuracy and better computation time than state-of-the-art approaches on test data from the Low Dose CT Challenge dataset without increasing reprojection error.This work was partly supported by RFBR (grants) 18-29-26020 and 19-01-00790

Algorithm for post-processing of tomography images to calculate the dimension-geometric features of porous structures

An algorithm for post-processing of the grayscale 3D computed tomography (CT) images of porous structures with the automatic selection of filtering parameters is proposed. The determination of parameters is carried out on a representative part of the image under analysis. A criterion for the search for optimal filtering parameters based on the count of "levitating stone" voxels is described. The stages of CT image filtering and its binarization are performed sequentially. Bilateral and anisotropic diffuse filtering is implemented; the Otsu method for unbalanced classes is chosen for binarization. Verification of the proposed algorithm was carried out on model data. To create model porous structures, we used our image generator, which implements the function of anisotropic porous structures generation. Results of the post-processing of real CT images containing noise and reconstruction artifacts by the proposed method are discussed.This work was partly supported by the RF Ministry of Science and Higher Education within the State assignment of the FSRC "Crystallography and Photonics" RAS (computed tomography measurements and data analysis) and the Russian Foundation for Basic Research (RFBR) under projects Nos. 18-29-26019 and 19-01-00790 (algorithms development)

Towards monitored tomographic reconstruction: algorithm-dependence and convergence

The monitored tomographic reconstruction (MTR) with optimized photon flux technique is a pioneering method for X-ray computed tomography (XCT) that reduces the time for data acquisition and the radiation dose. The capturing of the projections in the MTR technique is guided by a scanning protocol built on similar experiments to reach the predetermined quality of the reconstruction. This method allows achieving a similar average reconstruction quality as in ordinary tomography while using lower mean numbers of projections. In this paper, we, for the first time, systematically study the MTR technique under several conditions: reconstruction algorithm (FBP, SIRT, SIRT-TV, and others), type of tomography setup (micro-XCT and nano-XCT), and objects with different morphology. It was shown that a mean dose reduction for reconstruction with a given quality only slightlyvaries with choice of reconstruction algorithm, and reach up to 12.5 % in case of micro-XCT and 8.5 % for nano-XCT. The obtained results allow to conclude that the monitored tomographic reconstruction approach can be universally combined with an algorithm of choice to perform a controlled trade-off between radiation dose and image quality. Validation of the protocol on independent common ground truth demonstrated a good convergence of all reconstruction algorithms within the MTR protocol.This work was partly supported by RFBR (grants) 20-07-00934

Lattice vibrations of alpha'-NaV_2O_5 in the low-temperature phase. Magnetic bound states?

We report high resolution polarized infrared studies of the quarter-filled spin ladder compound alpha'-NaV_2O_5 as a function of temperature (5K <= T <= 300K). Numerous new modes were detected below the temperature T_c=34K of the phase transition into a charge ordered nonmagnetic state accompanied by a lattice dimerization. We analyse the Brillouin zone (BZ) folding due to lattice dimerization at T_c and show that some peculiarities of the low-temperature vibrational spectrum come from quadruplets folded from the BZ point (1/2, 1/2, 1/4). We discuss an earlier interpretation of the 70, 107, and 133cm-1 modes as magnetic bound states and propose the alternative interpretation as folded phonon modes strongly interacting with charge and spin excitations.Comment: 15 pages, 13 Postscript figure

Neural network regularization in the problem of few-view computed tomography

The computed tomography allows to reconstruct the inner morphological structure of an object without physical destructing. The accuracy of digital image reconstruction directly depends on the measurement conditions of tomographic projections, in particular, on the number of recorded projections. In medicine, to reduce the dose of the patient load there try to reduce the number of measured projections. However, in a few-view computed tomography, when we have a small number of projections, using standard reconstruction algorithms leads to the reconstructed images degradation. The main feature of our approach for few-view tomography is that algebraic reconstruction is being finalized by a neural network with keeping measured projection data because the additive result is in zero space of the forward projection operator. The final reconstruction presents the sum of the additive calculated with the neural network and the algebraic reconstruction. First is an element of zero space of the forward projection operator. The second is an element of orthogonal addition to the zero space. Last is the result of applying the algebraic reconstruction method to a few-angle sinogram. The dependency model between elements of zero space of forward projection operator and algebraic reconstruction is built with neural networks. It demonstrated that realization of the suggested approach allows achieving better reconstruction accuracy and better computation time than state-of-the-art approaches on test data from the Low Dose CT Challenge dataset without increasing reprojection error

Быстрый алгоритм расчета лучевых сумм в задаче компьютерной томографии

K.B. Bulatov1,2, M.V. Chukalina3,4, D.P. Nikolaev4 1Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Moscow, Russian Federation 2Smart Engines Service LLC, Moscow, Russian Federation 3FSRC “Crystallography and Photonics” of the Russian Academy of Sciences, Moscow, Russian Federation 4Institute for Information Transmission Problems of the Russian Academy of Sciences, Moscow, Russian Federation E-mails: [email protected], [email protected], [email protected]. К.Б. Булатов1,2, М.В. Чукалина3,4, Д.П. Николаев4 1Федеральный исследовательский центр ≪Информатика и управление≫ РАН, г. Москва, Российская Федерация 2ООО ≪Смарт Энджинс Сервис≫, г. Москва, Российская Федерация 3Институт кристаллографии им. А.В. Шубникова ФНИЦ ≪Кристаллография и фотоника≫ РАН, г. Москва, Российская Федерация 4Институт проблем передачи информации РАН, г. Москва, Российская ФедерацияIn iterative methods of computed tomography, each iteration requires to calculate a multitude of sums over values for the current reconstruction approximation. Each summable set is an approximation of a straight line in the three-dimensional space. In a cone-beam tomography, the number of sums to be calculated on each iteration has a cubic dependence on the linear size of the reconstructed image. Direct calculation of these sums requires the number of summations in a quartic dependence on the linear image size, which limits the performance of the iterative methods. The novel algorithm proposed in this paper approximates the three-dimensional straight lines using dyadic patterns, and, using the adjustment of precalculation and inference complexity similar to the adjustment employed in the Method of Four Russians, provides the calculation of these sums with a sub-quartic dependence on the linear size of the reconstructed image. В итерационных методах компьютерной томографии на каждой итерации требует- ся расчет большого числа сумм значений текущего приближения реконструкции, причем каждое суммируемое множество приближает ту или иную прямую в трехмерном пространстве. При конической схеме сборки томографических проекций количество сумм, которое необходимо рассчитать на каждой итерации алгоритма, кубически зависит от линейного размера реконструируемого изображения. Прямой расчет такого числа сумм требует количество операций, которое находится в полиномиальной зависимости четвертой степени от линейного размера изображения, что ограничивает быстродействие итерационных методов. Предлагаемый в данной работе новый алгоритм использует приближение трехмерной прямой диадическим паттерном и, используя выравнивание трудоемкостей предподсчета и вывода, аналогичное применяемому в методе четырех русских, позволяет достичь полиномиальной зависимости от размера изображения меньшей степени, чем четыре, при расчете необходимых сумм.This work was partially financially supported by the Russian Foundation for Basic Research, projects 18-29-26020 and 18-29-26027