Limited Number Of Projections Research Articles

PNMC: Four-dimensional conebeam CT reconstruction combining prior network and motion compensation

Four-dimensional conebeam computed tomography (4D CBCT) is an efficient technique to overcome motion artifacts caused by organ motion during breathing. 4D CBCT reconstruction in a single scan usually divides projections into different groups of sparsely sampled data based on the respiratory phases. The reconstructed images within each group present poor image quality due to the limited number of projections. To improve the image quality of 4D CBCT in a single scan, we propose a novel reconstruction scheme that combines prior knowledge with motion compensation. We apply the reconstructed images of the full projections within a single routine as prior knowledge, providing structural information for the network to enhance the restoration structure. The prior network (PN-Net) is proposed to extract features of prior knowledge and fuse them with the sparsely sampled data using an attention mechanism. The prior knowledge guides the reconstruction process to restore the approximate organ structure and alleviates severe streaking artifacts. The deformation vector field (DVF) extracted using deformable image registration among different phases is then applied in the motion-compensated ordered-subset simultaneous algebraic reconstruction algorithm to generate 4D CBCT images. Proposed method has been evaluated using simulated and clinical datasets and has shown promising results by comparative experiment. Compared with previous methods, our approach exhibits significant improvements across various evaluation metrics.

Оптическая гильберт-томография газовых струй

Hilbert-optics and signal conversion methods form the basis for modern information and measurement technologies. The Hilbert transform in the frequency space is physically reduced to a certain phase transformation of the Fourier spectrum of the signal in a wide frequency band. The article discusses the possibility of Hilbert tomography using the example of studying the isothermal flow of a freon-22 jet. An optical system based on the IAB-463M modernized wide-aperture shadow device has been developed. This system makes it possible to perform four-angle diagnostics of the studied phase object using probing light beams. The beams orientation is defined at angles of 0, π/2, π/4 and 3π/4 to the optical axis of the shadow device. This makes it possible to simultaneously register all four tomographic projections in the form of Hilbert images in separate sections of the CCD-matrix of the high-speed camera. The use of the iterative Gershberg-Papulis scheme for finding the parameters of the medium under study based on Hilbert tomography data is further proposed. This algorithm for reconstructing a function from its Radon data obtained by a limited number of projections consists in iterative transitions from estimating the function in the Fourier plane to its estimate in the spatial domain, corrected based on a priori information. The spectrum of the restored function is determined on the entire frequency plane as a result of an iterative process, which makes it possible to determine the values of the required function.

Accurate real space iterative reconstruction (RESIRE) algorithm for tomography

Tomography has made a revolutionary impact on the physical, biological and medical sciences. The mathematical foundation of tomography is to reconstruct a three-dimensional (3D) object from a set of two-dimensional (2D) projections. As the number of projections that can be measured from a sample is usually limited by the tolerable radiation dose and/or the geometric constraint on the tilt range, a main challenge in tomography is to achieve the best possible 3D reconstruction from a limited number of projections with noise. Over the years, a number of tomographic reconstruction methods have been developed including direct inversion, real-space, and Fourier-based iterative algorithms. Here, we report the development of a real-space iterative reconstruction (RESIRE) algorithm for accurate tomographic reconstruction. RESIRE iterates between the update of a reconstructed 3D object and the measured projections using a forward and back projection step. The forward projection step is implemented by the Fourier slice theorem or the Radon transform, and the back projection step by a linear transformation. Our numerical and experimental results demonstrate that RESIRE performs more accurate 3D reconstructions than other existing tomographic algorithms, when there are a limited number of projections with noise. Furthermore, RESIRE can be used to reconstruct the 3D structure of extended objects as demonstrated by the determination of the 3D atomic structure of an amorphous Ta thin film. We expect that RESIRE can be widely employed in the tomography applications in different fields. Finally, to make the method accessible to the general user community, the MATLAB source code of RESIRE and all the simulated and experimental data are available at https://zenodo.org/record/7273314.

Assessment of the impact of noise level on the accuracy of reconstruction of the image of the industrial product

The traditional tomography is an effective remedy for medical diagnostics, nondestructive control of industrial designs and for quality check of industrial products. Tomographic visualization of objects in case of an incomplete viewing angle, limited number of projections and/or the insufficient power of a source of x-ray radiation is strongly incorrect return task. Article is devoted to case research when noise in input data significantly affect convergence and quality of the reconstructed image.

Super-resolution computed tomography imaging spectrometry

Computed tomography imaging spectrometry (CTIS) is a snapshot spectral imaging technique that relies on a limited number of projections of the target data cube (2D spatial and 1D spectral), which can be reconstructed via a delicate tomographic reconstruction algorithm. However, the restricted angle difference between the projections and the space division multiplexing of the projections make the reconstruction suffer from severe artifacts as well as a low spatial resolution. In this paper, we demonstrate super-resolution computed tomography imaging spectrometry (SRCTIS) by assimilating the information obtained by a conventional CTIS system and a regular RGB camera, which has a higher pixel resolution. To improve the reconstruction accuracy of CTIS, the unique information provided by the zero-order diffraction of the target scene is used as a guidance image for filtering to better preserve the edges and reduce artifacts. The recovered multispectral image is then mapped onto the RGB image according to camera calibration. Finally, based on the spectral and the spatial continuities of the target scene, the multispectral information obtained from CTIS is propagated to each pixel of the RGB image to enhance its spectral resolution, resulting in SRCTIS. Both stimulative studies and proof-of-concept experiments were then conducted, and the results quantified by key metrics, such as structural similarity index measurement and spectral angle mapping have suggested that the developed method cannot only suppress the reconstruction artifacts, but also simultaneously achieve high spatial and spectral resolutions.

Augmented light field tomography through parallel spectral encoding.

Snapshot recording of transient dynamics in three dimensions (3-D) is highly demanded in both fundamental and applied sciences. Yet it remains challenging for conventional high-speed cameras to address this need due to limited electronic bandwidth and reliance on mechanical scanning. The emergence of light field tomography (LIFT) provides a new solution to these long-standing problems and enables 3-D imaging at an unprecedented frame rate. However, based on sparse-view computed tomography, LIFT can accommodate only a limited number of projections, degrading the resolution in the reconstructed image. To alleviate this problem, we herein present a spectral encoding scheme to significantly increase the number of allowable projections in LIFT while maintaining its snapshot advantage. The resultant system can record 3-D dynamics at a kilohertz volumetric frame rate. Moreover, by using a multichannel compressed sensing algorithm, we improve the image quality with an enhanced spatial resolution and suppressed aliasing artifacts.

Low-dose Cone-Beam Computed Tomography Reconstruction through a fast Three-Dimensional Compressed Sensing Method Based on the Three-Dimensional Pseudo-polar Fourier Transform.

Background:Reconstruction of high quality two dimensional images from fan beam computed tomography (CT) with a limited number of projections is already feasible through Fourier based iterative reconstruction method. However, this article is focused on a more complicated reconstruction of three dimensional (3D) images in a sparse view cone beam computed tomography (CBCT) by utilizing Compressive Sensing (CS) based on 3D pseudo polar Fourier transform (PPFT).Method:In comparison with the prevalent Cartesian grid, PPFT re gridding is potent to remove rebinning and interpolation errors. Furthermore, using PPFT based radon transform as the measurement matrix, reduced the computational complexity.Results:In order to show the computational efficiency of the proposed method, we compare it with an algebraic reconstruction technique and a CS type algorithm. We observed convergence in <20 iterations in our algorithm while others would need at least 50 iterations for reconstructing a qualified phantom image. Furthermore, using a fast composite splitting algorithm solver in each iteration makes it a fast CBCT reconstruction algorithm. The algorithm will minimize a linear combination of three terms corresponding to a least square data fitting, Hessian (HS) Penalty and l1 norm wavelet regularization. We named it PP-based compressed sensing-HS-W. In the reconstruction range of 120 projections around the 360° rotation, the image quality is visually similar to reconstructed images by Feldkamp-Davis-Kress algorithm using 720 projections. This represents a high dose reduction.Conclusion:The main achievements of this work are to reduce the radiation dose without degrading the image quality. Its ability in removing the staircase effect, preserving edges and regions with smooth intensity transition, and producing high-resolution, low-noise reconstruction results in low-dose level are also shown.

X-rays image reconstruction using proximal algorithm and adapted TV regularization

Computed tomography (CT) aims to reconstruct an internal distribution of an object based on projection measurements. In the case of a limited number of projections, the reconstruction problem becomes significantly ill-posed. Practically, reconstruction algorithms play a crucial role in overcoming this problem. In the case of missing or incomplete data, and in order to improve the quality of the reconstruction image, the choice of a sparse regularisation by adding l1 norm is needed. The reconstruction problem is then based on using proximal operators. We are interested in the Douglas-Rachford method and employ total variation (TV) regularization. An efficient technique based on these concepts is proposed in this study. The primary goal is to achieve high- quality reconstructed images in terms of PSNR parameter and relative error. The numerical simulation results demonstrate that the suggested technique minimizes noise and artifacts while preserving structural information. The results are encouraging and indicate the effectiveness of the proposed strategy.

Transition to mammography in the regular computed tomography simulation and reconstruction software

This paper presents a modification of the previously developed and maintained computed tomography simulation and reconstruction software for the mammography case. New additional modules are designed to process the mammography data. Mammography provides incomplete information about the subject taken from the limited number points of view but as a result has potentially minimized exposure to radiation for the biological tissue under study. We implement this method by providing new standalone independent mammography modules in our software package. These modules are responsible for creating the projections’ set according to the operator’s input of exposure angles, phantom’s structure, and other multiple recording parameters. These additional modules reconstruct the data from these generated sets of projections or take the real medical data as input. Contrast and features’ recognition are particularly important elements of the study due to the limited number of projections in set. Our software could be used in combination with any real commercial mammography scanner as well as for research purposes to train medical and physics personnel and study for novel methods of contrast and image enhancement.

NUDIM: A non-uniform fast Fourier transform based dual-space constraint iterative reconstruction method in biological electron tomography

Electron tomography, a powerful imaging tool for studying 3D structures of macromolecular assemblies, always suffers from imperfect reconstruction with limited resolution due to the intrinsic low signal-to-noise ratio (SNR) and inaccessibility to certain tilt angles induced by radiation damage or mechanical limitation. In order to compensate for such insufficient data with low SNR and further improve imaging resolution, prior knowledge constraints about the objects in both real space and reciprocal space are thus exploited during tomographic reconstruction. However, direct Fast Fourier transform (FFT) between real space and reciprocal space remains extraordinarily challenging owing to their inconsistent grid sampling modes, e.g. regular and uniform grid sampling in real space whereas radial or polar grid sampling in reciprocal space. In order to solve such problem, a technique of non-uniform fast Fourier transform (NFFT) has been developed to transform efficiently between non-uniformly sampled grids in real and reciprocal space with sufficient accuracy. In this work, a Non-Uniform fast Fourier transform based Dual-space constraint Iterative reconstruction Method (NUDIM) applicable to biological electron tomography is proposed with a combination of basic concepts from equally sloped tomography (EST) and NFFT based reconstruction. In NUDIM, the use of NFFT can circumvent such grid sampling inconsistency and thus alleviate the stringent equally-sloped sampling requirement in EST reconstruction, while the dual-space constraint iterative procedure can dramatically enhance reconstruction quality. In comparison with conventional reconstruction methods, NUDIM is numerically and experimentally demonstrated to produce superior reconstruction quality with higher contrast, less noise and reduced missing wedge artifacts. More importantly, it is also capable of retrieving part of missing information from a limited number of projections.

Gradient-based and wavelet-based compressed sensing approaches for highly undersampled tomographic datasets

Electron tomography is widely employed for the 3D morphological characterization at the nanoscale. In recent years, there has been a growing interest in analytical electron tomography (AET) as it is capable of providing 3D information about the elemental composition, chemical bonding and optical/electronic properties of nanomaterials. AET requires advanced reconstruction algorithms as the datasets often consist of a very limited number of projections. Total variation (TV)-based compressed sensing approaches were shown to provide high-quality reconstructions from undersampled datasets, but staircasing artefacts can appear when the assumption about piecewise constancy does not hold. In this paper, we compare higher-order TV and wavelet-based approaches for AET applications and provide an open-source Python toolbox, Pyetomo, containing 2D and 3D implementations of both methods. A highly sampled STEM-HAADF dataset of an Er-doped porous Si sample and a heavily undersampled STEM-EELS dataset of a Ge-rich GeSbTe (GST) thin film annealed at 450°C are used to evaluate the performance of the different approaches. We show that polynomial annihilation with order 3 (HOTV3) and the Bior4.4 wavelet outperform the classical TV minimization and the related Haar wavelet.

X-rays Image reconstruction using Proximal Algorithm and adapted TV Regularization

Computed tomography (CT) aims to reconstruct an internal distribution of an object based on projection measurements. In the case of a limited number of projections, the reconstruction problem becomes significantly ill-posed. Practically, reconstruction algorithms play a crucial role in overcoming this problem. In the case of missing or incomplete data, and in order to improve the quality of the reconstruction image, the choice of a sparse regularisation by adding l1 norm is needed. The reconstruction problem is then based on using proximal operators. We are interested in the Douglas-Rachford method and employ total variation (TV) regularization. An efficient technique based on these concepts is proposed in this study. The primary goal is to achieve high-quality reconstructed images in terms of PSNR parameter and relative error. The numerical simulation results demonstrate that the suggested technique minimizes noise and artifacts while preserving structural information. The results are encouraging and indicate the effectiveness of the proposed strategy.

Direct Iterative Reconstruction of Computed Tomography Trajectories Reconstruction from limited number of projections with DIRECTT.

X-ray computed tomography has many applications in materials science and non-destructive testing. While the standard filtered back-projection reconstruction of the radiographic datasets is fast and simple, it typically fails in returning accurate results from missing or inconsistent projections. Among the alternative techniques that have been proposed to handle such data is the Direct Iterative REconstruction of Computed Tomography Trajectories (DIRECTT) algorithm. We describe a new approach to the algorithm, which significantly decreases the computational time while achieving a better reconstruction quality than that of other established algorithms.

Limited Angle Tomography reconstruction for non-standard MBI system by means of parallel-hole and pinhole optics

The purpose of the present work is the study of reconstruction properties of a new Molecular Breast Imaging (MBI) device for the early diagnosis of breast cancer, in Limited Angle Tomography (LAT), by using two asymmetric detector heads with different collimators. The detectors face each other in anti-parallel viewing direction and, mild-compressing the breast phantom, they are able to reconstruct the inner tumour of the phantoms with only a limited number of projections using a dedicated maximum-likelihood expectation maximization algorithm. The phantoms, the MBI system, as well as the Monte Carlo simulator, are briefly described. The MBI system's model has been implemented in IDL, in order to evaluate the best LAT configuration of the system and its reconstruction ability by varying tumour's size, depth and uptake. The LAT setup in real and simulated configurations, as well as the maximum-likelihood method and the preliminary reconstruction results, are discussed.

Fast binary CT using Fourier null space regularization (FNSR)

X-ray CT is increasingly being adopted in manufacturing as a non destructive inspection tool. Traditionally, industrial workflows follow a two step procedure of reconstruction followed by segmentation. Such workflows suffer from two main problems: (1) the reconstruction typically requires thousands of projections leading to increased data acquisition times. (2) The application of the segmentation process a posteriori is dependent on the quality of the original reconstruction and often does not preserve data fidelity. We present a fast iterative x-ray CT method which simultaneously reconstructs and segments an image from a limited number of projections called Fourier null space regularization (FNSR). The novelty of the approach is in the explicit updating of the image null space with values derived from a regularized image from the previous iteration, thus compensating for any missing projections and effectively regularizing the reconstruction. The speed of the method is achieved by directly applying the Fourier Slice Theorem where the non-uniform fast Fourier transform (NUFFT) is used to compute the frequency spectrum of the projections at their positions in the image k-space. At each iteration a segmented image is computed which is used to populate the null values of the image k-space effectively steering the reconstruction towards a binary solution. The effectiveness of the method to generate accurate reconstructions is demonstrated and benchmarked against other iterative reconstruction techniques using a series of numerical examples. Finally, FNSR is validated using industrial x-ray CT data where accurate reconstructions were achieved with 18 or more projections, a significant reduction from the 5000 needed by filtered back projection.

An Exact and Fast CBCT Reconstruction via Pseudo-Polar Fourier Transform based Discrete Grangeat's Formula.

The recent application of Fourier Based Iterative Reconstruction Method (FIRM) has made it possible to achieve high-quality 2D images from a fan beam Computed Tomography (CT) scan with a limited number of projections in a fast manner. The proposed methodology in this article is designed to provide 3D Radon space in linogram fashion to facilitate the use of FIRM with cone beam projections (CBP) for the reconstruction of 3D images in a sparse view angles Cone Beam CT (CBCT). For this reason, in the first phase, the 3D Radon space is generated using CBP data after discretization and optimization of the famous Grangeat's formula. The method used in this process involves fast Pseudo Polar Fourier transform (PPFT) based on 2D and 3D Discrete Radon Transformation (DRT) algorithms with no wraparound effects. In the second phase, we describe reconstruction of the objects with available Radon values, using direct inverse of 3D PPFT. The method presented in this section eliminates noises caused by interpolation from polar to Cartesian space and exhibits no thorn, V-shaped and wrinkle artifacts. This method reduces the complexity to for images of size n × n × n The Cone to Radon conversion (Cone2Radon) Toolbox in the first phase and MATLAB/ Python toolbox in the second phase were tested on three digital phantoms and experiments demonstrate fast and accurate cone beam image reconstruction due to proposed.

Constrained Discriminative Projection Learning for Image Classification.

Projection learning is widely used in extracting discriminative features for classification. Although numerous methods have already been proposed for this goal, they barely explore the label information during projection learning and fail to obtain satisfactory performance. Besides, many existing methods can learn only a limited number of projections for feature extraction which may degrade the performance in recognition. To address these problems, we propose a novel constrained discriminative projection learning (CDPL) method for image classification. Specifically, CDPL can be formulated as a joint optimization problem over subspace learning and classification. The proposed method incorporates the low-rank constraint to learn a robust subspace which can be used as a bridge to seamlessly connect the original visual features and objective outputs. A regression function is adopted to explicitly exploit the class label information so as to enhance the discriminability of subspace. Unlike existing methods, we use two matrices to perform feature learning and regression, respectively, such that the proposed approach can obtain more projections and achieve superior performance in classification tasks. The experiments on several datasets show clearly the advantages of our method against other state-of-the-art methods.

A Soft-Threshold Filtering Approach for Tomography Reconstruction from a Limited Number of Projections with Bilateral Edge Preservation.

In X-ray tomography image reconstruction, one of the most successful approaches involves a statistical approach with norm for fidelity function and some regularization function with norm, . Among them stands out, both for its results and the computational performance, a technique that involves the alternating minimization of an objective function with norm for fidelity and a regularization term that uses discrete gradient transform (DGT) sparse transformation minimized by total variation (TV). This work proposes an improvement to the reconstruction process by adding a bilateral edge-preserving (BEP) regularization term to the objective function. BEP is a noise reduction method and has the purpose of adaptively eliminating noise in the initial phase of reconstruction. The addition of BEP improves optimization of the fidelity term and, as a consequence, improves the result of DGT minimization by total variation. For reconstructions with a limited number of projections (low-dose reconstruction), the proposed method can achieve higher peak signal-to-noise ratio (PSNR) and structural similarity index measurement (SSIM) results because it can better control the noise in the initial processing phase.

XAP-Lab: A software tool for designing flexible X-ray acquisition protocols

Background and objectiveThe availability of digital X-ray detectors, together with the development of new robotized hardware and reconstruction algorithms, opens the opportunity to provide 3D capabilities with conventional radiology systems. This would be based on the acquisition of a limited number of projections with non-standard geometrical configurations. The versatility of these techniques is enormous, enabling the introduction of tomography in situations where a CT system is hardly available, such as during surgery or in an ICU, or in which a reduction of radiation dose is key, as in pediatrics. Computer simulations are a valuable tool to explore these possibilities before their actual implementation on real systems. Existing software tools generally simulate only standard acquisition protocols, such as cone-beam with circular trajectory, thus not allowing the users to evaluate more sophisticated projection geometries. The goal of this work is to design a simulation tool that enables the design of acquisition protocols with flexible projection geometries. MethodsWe present XAP-Lab, a software tool for the design of X-ray acquisition protocols with flexible trajectories. For a given projection geometry, defined through a graphical user interface, it allows the user to simulate projections using GPU-accelerated kernels, the visualization of the scanned field of view and the estimation of the total radiation dose. The complete acquisition protocol can then be exported with the appropriate format for its use on real systems.We tested the software by optimizing a tomosynthesis protocol and validating the results with real acquisitions using a SEDECAL NOVA FA radiography system and phantoms for quantitative and qualitative evaluation. ResultsQuantitative evaluation using a phantom showed a mean error under 4 mm for each position, below the ±5 mm tolerance of the system specified by the manufacturer. Visual evaluation on a thorax acquisition also showed a good geometrical agreement between simulated and real projections. ConclusionsResults showed an excellent matching with simulations, supporting the usefulness of XAP-Lab for the design of new acquisition protocols with non-standard geometries.

McSART: an iterative model-based, motion-compensated SART algorithm for CBCT reconstruction

4D cone beam computed tomography (CBCT) images of the thorax and abdomen can have reduced quality due to the limited number of projections per respiratory bin used in gated image reconstruction. In this work, we present a new algorithm to reconstruct high quality CBCT images by simultaneously reconstructing images and generating an associated respiratory motion model. This is done by updating model parameters to compensate for motion during the iterative image reconstruction process. CBCT image acquisition was simulated using the digital eXternal CArdiac Torso (XCAT) phantom, simulating breathing motion using four patient breathing traces. 4DCBCT images were reconstructed using the simultaneous algebraic reconstruction technique (SART), and compared to the proposed motion-compensated SART (McSART) algorithm. McSART used a motion model that describes tissue position as a function of diaphragm amplitude and velocity. The McSART algorithm alternately updated the motion model and image reconstruction, increasing the number of projections used for image reconstruction with every iteration. The model was able to interpolate and extrapolate deformations according to the magnitude of the surrogate signal. Without noise, the final iteration McSART images had HU errors at 31%, 34%, and 44% of their SART-reconstructed counterparts compared to ground truth XCAT images, with corresponding root-mean-square (RMS) motion model errors of 0.75 mm, 1.08 mm, and 1.17 mm respectively. With added image noise, McSART’s HU error was 31% of the SART-reconstructed 4DCBCT error, with a 1.43 mm RMS motion model error. Qualitatively, blurring and streaking artifacts were reduced in all the reconstructed images compared to 3D or SART-reconstructed 4DCBCT. The output of the algorithm was a high quality reference image and a corresponding motion model, that could be used to deform the reference image to any other point in a breathing cycle.