Shepp-Logan Phantom Research Articles

Methods for Reducing Ring Artifacts in Tomographic Images Using Wavelet Decomposition and Averaging Techniques

Computed tomography (CT) is one of the fundamental imaging modalities used in medicine, allowing for the acquisition of accurate cross-sectional images of internal body tissues. However, during the acquisition and reconstruction process, various artifacts can arise, and one of them is ring artifacts. These artifacts result from the inherent limitations of CT scanner components and the properties of the scanned material, such as detector defects, non-uniform distribution of radiation from the source, or the presence of metallic elements within the scanning region. The purpose of this study was to identify and reduce ring artifacts in tomographic images using image decomposition and average filtering methods. In this study, tests were conducted on the effectiveness of identifying ring artifacts using wavelet decomposition methods for images. The test was performed on a Shepp–Logan phantom with implemented artifacts of different intensity levels. The analysis was performed using different wavelet families, and linear approximation methods were used to filter the image in the identified areas. Additional filtering was performed using moving average methods and empirical mode decomposition (EMD) techniques. Image comparison methods, i.e., RMSE, SSIM and MS-SSIM, were used to evaluate performance. The results of this study showed a significant improvement in the quality of tomographic phantom images. The authors obtained more than 50% improvement in image quality with reference to the image without any filtration. The different wavelet families had different efficiencies with relation to the identification of the induction regions of ring artifacts. The Haar wavelet and Coiflet 1 showed the best performance in identifying artifact induction regions, with comparative RMSE values for these wavelets of 0.1477 for Haar and 0.1469 for Coiflet 1. The applied additional moving average filtering and EMD permitted us to improve image quality, which is confirmed by the results of the image comparison. The obtained results allow us to assess how the used methods affect the reduction in ring artifacts in phantom images with induced artifacts.

Reconstruction of Tomographic Size Using a Filtered Back Projection Algorithm

Due to their widespread use, image processors are among the most essential computer processors. FBP technique is one of the most widely used tomographic reconstruction methods. Images from a computed tomography (CT) scanner with 512x512 pixels of raw data for parallel beam projections are the metadata to which this approach is applied. This work is divided into three parts. Several projections are created from an input test picture termed Shepp-Logan phantom in the first section, utilizing radon transformation. The picture is rebuilt from the projection of a parallel beam in the second section to minimize reconstruction time. Finally, the proposed system filters the projections using the Ram Lak filter and the Hann window in the third section to refine the picture and then recombine the projections to generate the reconstructed image. The reconstruction procedure is performed on CT images using a filtered back-projection algorithm in this article for image optimization and then projection recombination to generate the rebuilt picture. Since CT can accurately depict anatomical elements like bones and organs and may pick slides in any orientation, it is frequently used in biological applications and diagnostics. It also offers a great spatial resolution and soft tissue contrast. We develop, create, and run computer programs when we work with MATLAB. After projecting the 2D image onto a CT scanner, a very good result in reconstructing the image is received.

Reconstruction of Tomographic Size Using a Filtered Back Projection Algorithm

Due to their widespread use, image processors are among the most essential computer processors. FBP technique is one of the most widely used tomographic reconstruction methods. Images from a computed tomography (CT) scanner with 512x512 pixels of raw data for parallel beam projections are the metadata to which this approach is applied. This work is divided into three parts. Several projections are created from an input test picture termed Shepp-Logan phantom in the first section, utilizing radon transformation. The picture is rebuilt from the projection of a parallel beam in the second section to minimize reconstruction time. Finally, the proposed system filters the projections using the Ram Lak filter and the Hann window in the third section to refine the picture and then recombine the projections to generate the reconstructed image. The reconstruction procedure is performed on CT images using a filtered back-projection algorithm in this article for image optimization and then projection recombination to generate the rebuilt picture. Since CT can accurately depict anatomical elements like bones and organs and may pick slides in any orientation, it is frequently used in biological applications and diagnostics. It also offers a great spatial resolution and soft tissue contrast. We develop, create, and run computer programs when we work with MATLAB. After projecting the 2D image onto a CT scanner, a very good result in reconstructing the image is received.

Stability of the isotropic conductivity reconstruction using magnetic resonance electrical impedance tomography (MREIT)

Magnetic resonance electrical impedance tomography (MREIT) is a high-resolution imaging modality that aims to reconstruct the objects’ conductivity distributions at low frequency using the measurable z-component of the magnetic flux density obtained from an MRI scanner. Traditional reconstruction algorithms in MREIT use two datum subject to two linearly independent current densities. However, the temporal resolution of such a MREIT image is relatively low. Recently, a single current harmonic Bz algorithm has been proposed to improve the temporal resolution. Even though a series of reconstruction algorithms have been proposed in the last two decades, the theoretical studies of MREIT are still quite limited. This paper presents the stability theorems for two datum and a single data-based isotropic conductivity reconstruction using MREIT. Using the regularity theory of elliptic partial differential equations, we prove that the only instability in the inverse problem of MREIT comes from taking the second-order derivative of the measured data Bz , the z-component of the magnetic flux density. To get a stable reconstruction from the noisy Bz data, we note that the edge structure of ∇Bz reveals the edge features in the unknown conductivity and provides an edge-preserving denoising approach for the ∇Bz data. We use a modified Shepp–Logan phantom model to validate the proposed theory and the denoising approach.

Deep Image Prior-Based PET Reconstruction From Partial Data

In this paper, we propose an unsupervised deep learning method for positron emission tomography reconstruction (PET) from incomplete data. This method utilizes the so-called deep image prior (DIP) as an untrained deep convolutional neural network (CNN) to generate object reconstructions. The main idea is to re-parameterize the image reconstruction problem as a neural network optimization problem. We show that the proposed method effectively addresses the incomplete data reconstruction problem, which otherwise degrades the image resolution and quality of standard reconstruction algorithms. Meanwhile, the proposed method does not require any pre-training procedures, i.e., it is not biased toward any particular dataset. Hence, it has the potential to be used in clinical situations, where training data would be infeasible or prohibitively expensive. The performance of the proposed approach is evaluated with noisy synthetic data based on shepp-logan and brainweb phantoms, and clinical naive rat data. In addition, robustness studies of the approach with respect to regularization parameters are also carried out. We showcase that the proposed method considerably outperforms the state-of-the-art methods, leading to flexible reconstruction from incomplete PET data.

Quadratic Neural Networks for Solving Inverse Problems

In this paper we investigate the solution of inverse problems with neural network ansatz functions with generalized decision functions. The relevant observation for this work is that such functions can approximate typical test cases, such as the Shepp-Logan phantom, better, than standard neural networks. Moreover, we show that the convergence analysis of numerical methods for solving inverse problems with shallow generalized neural network functions leads to more intuitive convergence conditions, than for deep affine linear neural networks.

Sparse-view X-ray CT based on a box-constrained nonlinear weighted anisotropic TV regularization.

Sparse-view computed tomography (CT) is an important way to reduce the negative effect of radiation exposure in medical imaging by skipping some X-ray projections. However, due to violating the Nyquist/Shannon sampling criterion, there are severe streaking artifacts in the reconstructed CT images that could mislead diagnosis. Noting the ill-posedness nature of the corresponding inverse problem in a sparse-view CT, minimizing an energy functional composed by an image fidelity term together with properly chosen regularization terms is widely used to reconstruct a medical meaningful attenuation image. In this paper, we propose a regularization, called the box-constrained nonlinear weighted anisotropic total variation (box-constrained NWATV), and minimize the regularization term accompanying the least square fitting using an alternative direction method of multipliers (ADMM) type method. The proposed method is validated through the Shepp-Logan phantom model, alongisde the actual walnut X-ray projections provided by Finnish Inverse Problems Society and the human lung images. The experimental results show that the reconstruction speed of the proposed method is significantly accelerated compared to the existing $ L_1/L_2 $ regularization method. Precisely, the central processing unit (CPU) time is reduced more than 8 times.

A novel multi-agent genetic algorithm for limited-view computed tomography

Computed tomography (CT) is a non-invasive testing technique to generate the internal image of any object. It has various applications belonging to medical imaging and other engineering applications. The present article proposes a novel multiagent genetic algorithm based on hill-climbing for limited-view computed tomography (MAGAH-CT). The MAGAH combines a multi-agent system based on a genetic algorithm (MAGA) and a hill-climbing approach. The MAGAH uses multiple operators to refine the agent population during evolution. These operators are neighborhood-based competition, hybrid crossover, adaptive mutation, and self-learning. MAGAH-CT explores better solutions in neighborhood-based competition and cooperation operators. The self-learning operator learns through the agent’s population generated by adaptive mutation and hybrid crossover operator, ensuring the results’ continuity. The proposed algorithm has been tested on a Shepp-Logan head phantom with limited view projection data. The algorithm can accurately reconstruct the low-noise CT image using limited data constraints. Experimental results reveal that the presented MAGAH-CT algorithm is efficient and computationally reasonable. The presented algorithm is suitable for low-noise CT reconstruction and out-performs other limited-view CT reconstruction algorithms.

GROG-pCS: GRAPPA Operator Gridding with CS-based p-thresholding for Under-sampled Radially Encoded MRI

Major limitation of MRI is long scan time. Compressed Sensing (CS) is a contemporary technique used to accelerate MRI scan time. In CS, fully sampled MRI images are reconstructed from the partially acquired k-space data. In CS MRI, the utilization of a non-linear reconstruction algorithm is one of the key requirements for successful signal recovery. Numerous methods have been used in CS for solving the non-linear problems to get the solution image. In this paper, we proposed GRAPPA Operator gridding (GROG) with CS-based p-thresholding to reconstruct the artefact free MR images from the partially acquired radial k-space data. In this proposed scheme, initially radially acquired under-sampled k-space data is mapped onto Cartesian space using GROG gridding and then CS reconstruction is performed by using iterative p-thresholding. The proposed method is tested on four MRI data sets, (i) simulated Shepp-Logan phantom, (ii) 1.5T human brain data, (iii) 3T human brain, and (iv) 3T short-axial cardiac (SA) radial data. The reconstruction results are compared with the CS-based iterative hard-thresholding and soft-thresholding reconstructions. The quality of the solution images is evaluated by using (i) Artifact Power (AP), (ii) Root Mean Square Error (RMSE), and (iii) Peak Signal-to-Noise Ratio (PSNR).

Radon transform with Gaussian beam: Theoretical and numerical reconstruction scheme

The Radon transform and its various types have been studied since its introduction by Johann Radon in 1917. Since the Radon transform is an integral transform that maps a given function to its line integral, it has been studied in the field of computerized tomography, which deals with electromagnetic waves that primarily travel along straight lines, such as X-rays. However, in many laser optics applications, it is assumed that the laser beam is shaped like a Gaussian bell rather than a straight line. Therefore, in tomographic modalities using optical beams, such as optical projection tomography, images reconstructed with the inversion algorithms for the standard Radon transform are subject to a loss of quality. To address this issue, one needs to consider theoretical inversion methods for Radon transforms with Gaussian beam kernels and associated numerical reconstruction methods. In this study, we consider a Radon transform with a Gaussian beam kernel (also known as the point spread function) and show the uniqueness of the inversion of this transform. Furthermore, we provide an accurate and stable numerical reconstruction algorithm using the point spread function-sequential quadratic Hamiltonian scheme. Numerical experiments with disk and Shepp–Logan phantoms demonstrate that the proposed framework provides superior reconstructions compared to the traditional filtered back-projection algorithm.

BigBrain-MR: a new digital phantom with anatomically-realistic magnetic resonance properties at 100-µm resolution for magnetic resonance methods development

The benefits, opportunities and growing availability of ultra-high field magnetic resonance imaging (MRI) for humans have prompted an expansion in research and development efforts towards increasingly more advanced high-resolution imaging techniques. To maximize their effectiveness, these efforts need to be supported by powerful computational simulation platforms that can adequately reproduce the biophysical characteristics of MRI, with high spatial resolution. In this work, we have sought to address this need by developing a novel digital phantom with realistic anatomical detail up to 100-µm resolution, including multiple MRI properties that affect image generation. This phantom, termed BigBrain-MR, was generated from the publicly available BigBrain histological dataset and lower-resolution in-vivo 7T-MRI data, using a newly-developed image processing framework that allows mapping the general properties of the latter into the fine anatomical scale of the former. Overall, the mapping framework was found to be effective and robust, yielding a diverse range of realistic “in-vivo-like” MRI contrasts and maps at 100-µm resolution. BigBrain-MR was then tested in three imaging applications (motion effects and interpolation, super-resolution imaging, and parallel imaging reconstruction) to investigate its properties, value and validity as a simulation platform. The results consistently showed that BigBrain-MR can closely approximate the behavior of real in-vivo data, more realistically and with more extensive features than a more classic option such as the Shepp-Logan phantom. Its flexibility in simulating different contrast mechanisms and artifacts may also prove valuable for educational applications. BigBrain-MR is therefore deemed a favorable choice to support methodological development and demonstration in brain MRI, and has been made freely available to the community.

A machine learning supported sinogram interpolation method for X-ray computed tomography

The time of an X-ray Computed Tomography (XCT) measurement is directly affected by the number of acquired X-ray projections. In general, a large number of X-ray projections, hence a large acquisition time is required to obtain a qualitative reconstruction and successive feature analysis. To expand the applicability of XCT towards low-end parts we propose a novel sinogram interpolation method that incorporates the object rotation. The method combines a forward projection model of the XCT system and a deep learning regression model to generate intermediate X-ray projections for XCT scans with a reduced number of projections. Thereby, the accompanying reconstruction artefacts can be reduced while preserving a lower acquisition time. The method is validated on simulated projections of the 3D Shepp-Logan phantom and simulated projections of real 3D printed components using the ASTRA-toolbox. Within the reconstructions, less streaking artefacts are observed and an increased contrast between different features is obtained without introducing rotational artefacts.

Optimization of smoothing factor for fast non-local means algorithm in high pitch based low-dose computed tomography images with tin-filter

In this study, we applied the fast non-local means (FNLM) algorithm to high-pitch low-dose computed tomography (CT) images using a tin-filter. This study was conducted via a simulation study using a Shepp-Logan phantom and an experimental approach using American association of physicists in medicine (AAPM) phantom images. To optimize the smoothing factor of the FNLM algorithm, the values were adjusted from 0.01 to 0.05 at intervals of 0.001 and applied to the CT image. The smoothing factor of the optimal FNLM algorithm, derived through various quantitative evaluations, was 0.03. According to the results, when the optimized FNLM algorithm was applied to the acquired CT image with a low-dose protocol based on a high pitch condition, the estimated coefficient of variation, contrast-to-noise ratio, and signal-to-noise ratio were improved by 8.7, 6.7, and 8.0 times, respectively, compared to the general CT scanning condition (none). In addition, compared with the noise filtering methods mainly used in the past, both simulation and real experimental results proved that the application efficiency of the FNLM algorithm was high in the obtained low-dose-based CT images. In summary, the applicability of the FNLM algorithm in CT images obtained under low-dose conditions with high pitch using a tin-filter was demonstrated, and the derived research results are expected to be actively utilized in the diagnostic medical field to help reduce exposure doses and improve image quality.

Gradient-Based Pulsed Excitation and Relaxation Encoding in Magnetic Particle Imaging.

Magnetic particle imaging (MPI) is a radiation-free vessel- and target-imaging modality that can sensitively detect nanoparticles. A static magnetic gradient field, referred to as a selection field, is required in MPI to provide a field-free region (FFR) for spatial encoding. The image resolution of MPI is closely related to the size of the FFR, which is determined by the selection field gradient amplitude. Because of the limitations of existing gradient coil hardware, the image resolution of MPI cannot satisfy the clinical requirements of human in vivo imaging. Pulsed excitation has been confirmed to improve the image resolution of MPI by breaking down the 'relaxation wall.' This work proposes the use of a pulsed waveform magnetic gradient from magnetic resonance imaging to further improve the image resolution of MPI. Through alignment of the gradient direction along the field-free line (FFL), each location on the FFL is able to have a unique excitation field strength that generates a specific relaxation-induced decay signal. Through excitation of nanoparticles on the FFL with many gradient profiles, a high-resolution, one-dimensional (1D) image can be reconstructed on the FFL. For larger magnetic nanoparticles, simulation results revealed that a pulsed excitation field with a greater flat portion generates a 1D bar pattern phantom image with a higher correlation and spatial resolution. With parallel FFL and gradient coil movements, high-resolution, two-dimensional (2D) Shepp-Logan phantom and brain vessel maps were reconstructed through repetition of the spatially resolved measurement of magnetic nanoparticles on the FFL.

Noise correlation and its impact on the performance of multi-material decomposition-based spectral imaging in photon-counting CT.

It has been known that noise correlation plays an important role in the determination of the performance of spectral imaging based on two-material decomposition (2-MD). To further understand the basics of spectral imaging in photon-counting CT toward optimal design and implementation, we study the noise correlation in multi-MD (m-MD) and its impact on the performance of spectral imaging. We derive the equations that characterize the noise and noise correlation in the material-specific (basis) images in m-MD, followed by a simulation study to verify the derived equations and study the noise correlation's impact on the performance of spectral imaging. Using a specially designed digital phantom, the study of noise correlation runs over the cases of two-, three-, and four-MD (2-MD, 3-MD, and 4-MD). Then, the noise correlation's impact on the performance of spectral imaging in photon-counting CT is investigated, using a modified Shepp-Logan phantom. The results in 2-MD show that, in-line with what has been reported in the literature, the noise correlation coefficient between the material-specific images corresponding to the basis materials approaches -1. The results in m-MD (m≥3) are more complicated and interesting, as the noise correlation coefficients between a pair of the material-specific images alternate between ±1, and so do in the case of 4-MD. The m-MD data show that the noise in virtual monochromatic imaging (a form of spectral imaging) is moderate even though the noises in material-specific (basis) images vary drastically. The observation of noise correlation in 3-MD, 4-MD, and beyond (i.e., m-MD) is informative to the community. The relationship between noise correlation and the performance of spectral imaging revealed in this work may help clinical medical physicists understand the fundamentals of spectral imaging based on MD and optimize the performance of spectral imaging in photon-counting CT and other X-ray imaging modalities.

Cone-beam computed tomography based on truncated adaptive-weight total variation

It is challenging to get reconstruct high-quality images for a Computed laminography scan. CL images always suffer inter-slices aliasing and blurring since projections from the CL scanning are incomplete. To solve this problem, we propose an iterative reconstruction algorithm constrained by a truncated adaptive-weight total variation (TAwTV). In detail, the image gradient amplitude is first truncated according to a threshold, and then we design a cosine nonlinear function of truncated gradient amplitude to adjust the truncated gradient adaptively thus the truncated adaptive-weight total variation can overcome over-smoothing when penalizing larger gradient amplitude and isotropic property. Experiments on both simulated 3D printed circuit board, simulated workpiece and Shepp-Logan phantom show that the proposed algorithm has noticeable results in artifact suppression and edge-preserving.

A triple-source CT system for micro-scale investigation of geological materials: A simulation study

A triple-source CT system is proposed for micro-scale testing of geological materials. This study aims at reducing the projection acquisition time by two-thirds compared to a conventional single-source CT system. The proposed system with different positioning errors in the source-to-object distance (SOD) was simulated and tested using the Shepp-Logan phantom model, as well as slices of sand, glass beads, and concrete samples. Furthermore, the imaging quality of a single-source and the triple-source CT system with different dead detector pixels was compared. The results showed that within the maximum allowable positioning error, the pixel differences between the simulated and the original images are close to zero, and the structural similarities are greater than 0.96. In the presence of dead detector pixels, the quality of the simulated images in the triple-source CT system is superior to that of a single-source CT system. The presented triple-source CT system performs well in high-quality image reconstruction.

Virtual computed-tomography system for deep-learning-based material decomposition

Objective. Material decomposition (MD) evaluates the elemental composition of human tissues and organs via computed tomography (CT) and is indispensable in correlating anatomical images with functional ones. A major issue in MD is inaccurate elemental information about the real human body. To overcome this problem, we developed a virtual CT system model, by which various reconstructed images can be generated based on ICRP110 human phantoms with information about six major elements (H, C, N, O, P, and Ca). Approach. We generated CT datasets labelled with accurate elemental information using the proposed generative CT model and trained a deep learning (DL)-based model to estimate the material distribution with the ICRP110 based human phantom as well as the digital Shepp–Logan phantom. The accuracy in quad-, dual-, and single-energy CT cases was investigated. The influence of beam-hardening artefacts, noise, and spectrum variations were analysed with testing datasets including elemental density and anatomical shape variations. Main results. The results indicated that this DL approach can realise precise MD, even with single-energy CT images. Moreover, noise, beam-hardening artefacts, and spectrum variations were shown to have minimal impact on the MD. Significance. Present results suggest that the difficulty to prepare a large CT database can be solved by introducing the virtual CT system and the proposed technique can be applied to clinical radiodiagnosis and radiotherapy.

Drift Artifacts Correction for Laboratory Cone-Beam Nanoscale X-ray Computed Tomography by Fitting the Partial Trajectory of Projection Centroid

A self-correction method for the drift artifacts of laboratory cone-beam nanoscale X-ray computed tomography (nano-CT) based on the trajectory of projection centroid (TPC) is proposed. This method does not require additional correction phantoms, simplifying the correction process. The whole TPC is estimated by the partial TPC in the optimal projection set. The projection drift is calculated by the measured TPC and the estimated TPC. The interval search method is used so that the proposed method can adapt to the case of a truncated projection due to drift. The fixed-angle scanning experiment of the Siemens star and the partial derivative analysis of the projection position show the necessity of correcting drift artifacts. Further, the Shepp–Logan phantoms with different drift levels are simulated. The results show that the proposed method can effectively estimate the horizontal and vertical drifts within the projection drift range of ±2 mm (27 pixels) with high accuracy. Experiments were conducted on tomato seed and bamboo stick to validate the feasibility of the proposed method for samples with different textures. The correction effect on different reconstructed slices indicates that the proposed method provides performance superior to the reference scanning method (RSM) and global fitting. In addition, the proposed method requires no extra scanning, which improves the acquisition efficiency, as well as radiation utilization.

A supervised deep neural network approach with standardized targets for enhanced accuracy of IVIM parameter estimation from multi-SNR images.

Extraction of intravoxel incoherent motion (IVIM) parameters from noisy diffusion‐weighted (DW) images using a biexponential fitting model is computationally challenging, and the reliability of the estimated perfusion‐related quantities represents a limitation of this technique. Artificial intelligence can overcome the current limitations and be a suitable solution to advance use of this technique in both preclinical and clinical settings. The purpose of this work was to develop a deep neural network (DNN) approach, trained on numerical simulated phantoms with different signal to noise ratios (SNRs), to improve IVIM parameter estimation. The proposed approach is based on a supervised fully connected DNN having 3 hidden layers, 18 inputs and 3 targets with standardized values. 14 × 103 simulated DW images, based on a Shepp–Logan phantom, were randomly generated with varying SNRs (ranging from 10 to 100). 7 × 103 images (1000 for each SNR) were used for training. Performance accuracy was assessed in simulated images and the proposed approach was compared with the state‐of‐the‐art Bayesian approach and other DNN algorithms. The DNN approach was also evaluated in vivo on a high‐field MRI preclinical scanner. Our DNN approach showed an overall improvement in accuracy when compared with the Bayesian approach and other DNN methods in most of the simulated conditions. The in vivo results demonstrated the feasibility of the proposed approach in real settings and generated quantitative results comparable to those obtained using the Bayesian and unsupervised approaches, especially for D and f, and with lower variability in homogeneous regions. The DNN architecture proposed in this work outlines two innovative features as compared with other studies: (1) the use of standardized targets to improve the estimation of parameters, and (2) the implementation of a single DNN to enhance the IVIM fitting at different SNRs, providing a valuable alternative tool to compute IVIM parameters in conditions of high background noise.