Daniil Kazantsev

Employing temporal self-similarity across the entire time domain in computed tomography reconstruction

There are many cases where one needs to limit the X-ray dose, or the number of projections, or both, for high frame rate (fast) imaging. Normally, it improves temporal resolution but reduces the spatial resolution of the reconstructed data. Fortunately, the redundancy of information in the temporal domain can be employed to improve spatial resolution. In this paper, we propose a novel regularizer for iterative reconstruction of time-lapse computed tomography. The non-local penalty term is driven by the available prior information and employs all available temporal data to improve the spatial resolution of each individual time frame. A high-resolution prior image from the same or a different imaging modality is used to enhance edges which remain stationary throughout the acquisition time while dynamic features tend to be regularized spatially. Effective computational performance together with robust improvement in spatial and temporal resolution makes the proposed method a competitive tool to state-of-the-art techniques.

An Iterative CT Reconstruction Algorithm for Fast Fluid Flow Imaging

The study of fluid flow through solid matter by computed tomography (CT) imaging has many applications, ranging from petroleum and aquifer engineering to biomedical, manufacturing, and environmental research. To avoid motion artifacts, current experiments are often limited to slow fluid flow dynamics. This severely limits the applicability of the technique. In this paper, a new iterative CT reconstruction algorithm for improved a temporal/spatial resolution in the imaging of fluid flow through solid matter is introduced. The proposed algorithm exploits prior knowledge in two ways. First, the time-varying object is assumed to consist of stationary (the solid matter) and dynamic regions (the fluid flow). Second, the attenuation curve of a particular voxel in the dynamic region is modeled by a piecewise constant function over time, which is in accordance with the actual advancing fluid/air boundary. Quantitative and qualitative results on different simulation experiments and a real neutron tomography data set show that, in comparison with the state-of-the-art algorithms, the proposed algorithm allows reconstruction from substantially fewer projections per rotation without image quality loss. Therefore, the temporal resolution can be substantially increased, and thus fluid flow experiments with faster dynamics can be performed.

A novel technique to incorporate structural prior information into multi-modal tomographic reconstruction

There has been a rapid expansion of multi-modal imaging techniques in tomography. In biomedical imaging, patients are now regularly imaged using both single photon emission computed tomography (SPECT) and x-ray computed tomography (CT), or using both positron emission tomography and magnetic resonance imaging (MRI). In non-destructive testing of materials both neutron CT (NCT) and x-ray CT are widely applied to investigate the inner structure of material or track the dynamics of physical processes. The potential benefits from combining modalities has led to increased interest in iterative reconstruction algorithms that can utilize the data from more than one imaging mode simultaneously. We present a new regularization term in iterative reconstruction that enables information from one imaging modality to be used as a structural prior to improve resolution of the second modality. The regularization term is based on a modified anisotropic tensor diffusion filter, that has shape-adapted smoothing properties. By considering the underlying orientations of normal and tangential vector fields for two co-registered images, the diffusion flux is rotated and scaled adaptively to image features. The images can have different greyscale values and different spatial resolutions. The proposed approach is particularly good at isolating oriented features in images which are important for medical and materials science applications. By enhancing the edges it enables both easy identification and volume fraction measurements aiding segmentation algorithms used for quantification. The approach is tested on a standard denoising and deblurring image recovery problem, and then applied to 2D and 3D reconstruction problems; thereby highlighting the capabilities of the algorithm. Using synthetic data from SPECT co-registered with MRI, and real NCT data co-registered with x-ray CT, we show how the method can be used across a range of imaging modalities.

Temporal sparsity exploiting nonlocal regularization for 4D computed tomography reconstruction.

X-ray imaging applications in medical and material sciences are frequently limited by the number of tomographic projections collected. The inversion of the limited projection data is an ill-posed problem and needs regularization. Traditional spatial regularization is not well adapted to the dynamic nature of time-lapse tomography since it discards the redundancy of the temporal information. In this paper, we propose a novel iterative reconstruction algorithm with a nonlocal regularization term to account for time-evolving datasets. The aim of the proposed nonlocal penalty is to collect the maximum relevant information in the spatial and temporal domains. With the proposed sparsity seeking approach in the temporal space, the computational complexity of the classical nonlocal regularizer is substantially reduced (at least by one order of magnitude). The presented reconstruction method can be directly applied to various big data 4D (x, y, z+time) tomographic experiments in many fields. We apply the proposed technique to modelled data and to real dynamic X-ray microtomography (XMT) data of high resolution. Compared to the classical spatio-temporal nonlocal regularization approach, the proposed method delivers reconstructed images of improved resolution and higher contrast while remaining significantly less computationally demanding.

A Novel Tomographic Reconstruction Method Based on the Robust Student's t Function For Suppressing Data Outliers

Regularized iterative reconstruction methods in computed tomography can be effective when reconstructing from mildly inaccurate undersampled measurements. These approaches will fail, however, when more prominent data errors, or outliers, are present. These outliers are associated with various inaccuracies of the acquisition process: defective pixels or miscalibrated camera sensors, scattering, missing angles, etc. To account for such large outliers, robust data misfit functions, such as the generalized Huber function, have been applied successfully in the past. In conjunction with regularization techniques, these methods can overcome problems with both limited data and outliers. This paper proposes a novel reconstruction approach using a robust data fitting term which is based on the Students t distribution. This misfit promises to be even more robust than the Huber misfit as it assigns a smaller penalty to large outliers. We include the total variation regularization term and automatic estimation of a scaling parameter that appears in the Students t function. We demonstrate the effectiveness of the technique by using a realistic synthetic phantom and also apply it to a real neutron dataset.

Fan-beam tomography iterative algorithm based on Fourier transform

In tomography with a small number of views (i.e., optical tomography) there is a big demand for the algorithms able to adapt and efficiently use different types of a priori information about the solution. The Gerchberg-Papoulis algorithm (G-P) is known as one of the best iterative methods of a limited data tomography with parallel arrangement of projections because of its wide range of constraints it is capable to embed into processing steps. The G-P algorithm is based on the theorem of the central slice in Fourier space for parallel geometry of scanning and intensive interpolation in both image and frequency domains. In fan-beam geometry such algorithm has not been investigated, because of the central slice theorem lacking. In this paper recently developed theorem of the central slice is stated for fan-beam geometry, and on its basis the new iterative G-P algorithm is developed.

Synchrotron X-ray tomographic quantification of microstructural evolution in ice cream – a multi-phase soft solid

Microstructural evolution in soft matter directly influences not only the materials mechanical and functional properties, but also our perception of that materials taste. Using synchrotron X-ray tomography and cryo-SEM we investigated the time–temperature evolution of ice creams microstructure. This was enabled via three advances in synchrotron tomography: a bespoke tomography cold stage; improvements in pink beam in line phase contrast; and a novel image processing strategy for reconstructing and denoising in line phase contrast tomographic images. Using these three advances, we qualitatively and quantitatively investigated the effect of thermal changes on the ice creams microstructure after 0, 7 and 14 thermal cycles between −15 and −5 °C. The results demonstrate the effect of thermal cycling on the coarsening of both the air cells and ice crystals in ice cream. The growth of ice crystals almost ceases after 7 thermal cycles when they approach the size of the walls between air cells, while air cells continue to coarsen, forming interconnected channels. We demonstrate that the tomographic volumes provide a statistically more representative sample than cryo-SEM, and elucidate the three dimensional morphology and connectivity of phases. This resulted in new insights including the role of air cells in limiting ice crystal coarsening.

Sparsity seeking total generalized variation for undersampled tomographic reconstruction

Here we present a novel iterative approach for tomographic image reconstruction which improves image quality for undersampled and limited view projection measurements. Recently, the Total Generalized Variation (TGV) penalty has been proposed to establish a desirable balance between smooth and piecewise-constant solutions. Piecewise-smooth reconstructions are particularly important for biomedical applications, where the image surface slowly varies. The TGV penalty convexly combines the first and higher order derivatives, which means that for some regions (e.g. uniform background) it can be more challenging to find a sparser solution due to the weight of the higher order term. Therefore we propose a simple heuristic modification over the Chambolle-Pock reconstruction scheme for TGV which consists of adding the wavelet thresholding step which helps to suppress aliasing artifacts and noise while preserve piecewise-smooth appearance. Preliminary numerical results with two piecewise-smooth phantoms show strong improvement of the proposed method over TGV and TV penalties. The resulting images are smooth with sharp edges and fewer artifacts visible.

Multimodal Image Reconstruction Using Supplementary Structural Information in Total Variation Regularization

AbstractIn this paper, we propose an iterative reconstruction algorithm which uses available information from one dataset collected using one modality to increase the resolution and signal-to-noise ratio of one collected by another modality. The method operates on the structural information only which increases its suitability across various applications. Consequently, the main aim of this method is to exploit available supplementary data within the regularization framework. The source of primary and supplementary datasets can be acquired using complementary imaging modes where different types of information are obtained (e.g. in medical imaging: anatomical and functional). It is shown by extracting structural information from the supplementary image (direction of level sets) one can enhance the resolution of the other image. Notably, the method enhances edges that are common to both images while not suppressing features that show high contrast in the primary image alone. In our iterative algorithm we use available structural information within a modified total variation penalty term. We provide numerical experiments to show the advantages and feasibility of the proposed technique in comparison to other methods.

New iterative reconstruction methods for fan-beam tomography

Abstract In this paper, we present a novel class of iterative reconstruction methods for severely angular undersampled or/and limited-view tomographic problems with fan-beam scanning geometry. The proposed algorithms are based on a new analytical transform which generalizes Fourier-slice theorem to divergent-beam scanning geometries. Using a non-rigid coordinate transform, divergent rays can be reorganized into parallel ones. Therefore, one can employ a simpler parallel-beam projection model instead of more complicated divergent-beam geometries. Various existing iterative reconstruction techniques for divergent-beam geometries can be easily adapted to the proposed framework. The significant advantage of this formulation is the possibility of exploiting efficient Fourier-based recovery methods without rebinning of the projections. In case of highly sparse measurements (few-view data), rebinning methods are not suitable due to error-prone angular interpolation involved. In this work, three new methods based on the novel analytical framework for fan-beam geometry are presented: the Gerchberg-Papoulis algorithm, the Neumann decomposition method and its total variation regularized version. Presented numerical experiments demonstrate that the methods can be competitive in reconstructing from few-view noisy tomographic measurements.