Research On Image Reconstruction For Limited Angle CT Using Iterative Algorithm

Computed tomography (CT) imaging is the technique, where X-ray scans the object at different angles and then detector receives the attenuated X-ray, converting it into an electric signal, and transmitting the electric signal to the computer to get digitized projection data through the analog to digital conversion. After calculating the attenuation coefficient to obtain the two-dimensional distribution matrix by mathematics, electronic technology is applied to convert this distribution matrix into an image intensity distribution and get the tomographic image. Currently, CT is widely used in clinical medicine, industrial inspection, aerospace, biotechnology and other fields for its high resolution, specificity, non-destructive and other advantages, which is considered as one of the greatest inventions of the late 20th century. Its outstanding performance in clinical diagnosis is particularly prominent and widely used in inspection of the central nervous system, chest, large blood vessels and other parts of the diseases.CT image reconstruction algorithms are divided into two categories. The first category is analytic algorithm, which is based on Radon transform and has the advantages of strong theory basis and high speed reconstruction. Analytic reconstruction algorithm includes typical filtered back projection reconstruction algorithm (FBP) and three-dimensional FDK algorithm based on extended FBP. The flow of FBP algorithm is scanning the object to get projection data, and filtering the measured projection data, and finally back-projection the processed data to reconstruct image. This algorithm is widely used for its simplicity and fast reconstruction. FDK is a simple extension of the two-dimensional FBP algorithm and a three-dimensional tomography algorithm designed for cone beam circular orbit scan. FDK algorithm is characterized by excellent stability, convenience and practicality. If cone angle is small, better reconstructed images can be achieved and no significant artifacts produce. However, when the cone angle becomes large, reconstructed images will have clear image artifacts. The second category is iterative algorithm, which is based on discrete model. Iterative method can be divided into algebraic iterative algorithm and statistical iterative algorithm. Algebraic iterative algorithm is mainly represented by Algebraic Reconstruction Technique (ART) and Simultaneous Algebraic Reconstruction Technique (SART). The idea is discretizing initial image and assigning initial value of it, then calculate the estimated projection data according to the reconstruction model. Compare it with the measured projection data to correct the current estimated value. Finally, repeat the above process until approaching the real image. The basis of statistics iterative algorithm is that the photons received by detector are assumed approximately Poisson distribution after X-rays pass through the object, and image can be reconstructed from this statistical model. Maximum Likelihood-Expectation Maximization (ML-EM) is the widest method in statistics algorithms, which can overcome the interference of noise of projection data and reconstruct better images, but the convergence rate of ML-EM is slow.In order to reconstruct accurate image, we often need to scan complete projection data. But in practical applications, it’s difficult to obtain complete data due to some objective factors. These factors are mainly derived from X-ray dose. Because the X-ray is an ionizing radiation, more views data acquisition means the patients will receive more ionizing radiation, which can damage the body’s immune system, blood system, chromosome structure, etc., and increase the risk of cancer disease. Therefore, how to reduce the X-ray radiation dose and meanwhile guarantee the quality of the image has become a hot research.The methods of reducing X-ray radiation dose include adjusting the X-ray tube parameters, increasing the scan interval, reducing the scan range, etc. But decreasing the X-ray tube current will induce a lot of noise in projection data, resulting in noise significantly in reconstructed image, seriously affecting the image quality. Increasing the scan interval, also called sparse-view scan, lead to image reconstruction with obvious streak artifacts. Reducing the scan range, namely limited angle projection data, an effective way to reduce X-ray dose, will seriously affect the quality of reconstructed image, and have obvious geometric distortion. In this study, we focus on limited angle CT scanning modality to achieve the low dose reconstruction.Limited angle reconstruction is one type of CT reconstruction with incomplete projection data, and how to reconstruct high quality image in this case is concerned by many scholars. Analytic reconstruction algorithm demands higher completeness for projection data, and cannot bring in effective constraints in reconstruction process, so there are many artifacts in the limited angle CT reconstruction image. Iterative algorithm has been widely applied in the limited angle CT reconstruction with a lower requirement of projection data completeness, and easy to combine with a priori constraint. Donoho proposed compressive sensing theory to prove medical image or its gradient transformation is sparse. Minimizing the TV model can improve the image quality. Using this method is beneficial to superior image quality, but its rate of convergence is slow and a large number of iterations are needed.Our research of this paper is about how to reconstruct high quality image for limited-angle CT. Aiming at this problem, we studied the iterative algorithms, CS theories, prior information and the features of the initial image for iterative algorithms, and have acquired some research achievements.In this paper, firstly we introduce the development state of the CT and the research progress of the limited angle CT algorithm. Secondly, we present the hardware composition and imaging principle of the CT, the FBP algorithm and the FDK algorithm, the ART algorithm, the SART algorithm and the ML-ME algorithm. The simulation experiments indicate that the iterative reconstruction algorithm has a better image quality than the analytical reconstruction algorithm in limited angle CT. However, the iterative reconstruction algorithm still has some weakness to improve. We put forward two novel iterative algorithms for limited angle CT reconstruction to improve the image quality. They are shown in the following paragraphsFirst, ART-TV algorithm needs more than one thousand iterations to reconstruct high quality image and reconstruction time is long for limited angle CT. In order to solve this problem, we proposed a prior image constrained CT image reconstruction for limited angle CT. The prior image is a high-quality image which was obtained earlier from the same or other patient. Due to placing errors, organ motion deformation and other reasons, the anatomical structure location of the to-be-reconstructed image compared with prior image cannot be guaranteed to remain unchanged, thus many iterative reconstruction methods based on prior image fail in reconstructing satisfying images, or require time-consuming image registration. In the implementation process of our proposed algorithm, the average value of each homogeneous substance in prior image as prior information is considered, and then a new reconstruction model for limited angle CT is created to constrain the reconstruction image. This model simultaneously uses gradient information and prior knowledge of the image. Simulation experiments of Shepp-Logan phantom are performed by different algorithms. The experimental results show the prior image constrained CT image reconstruction method for limited angle data can improve the signal to noise ratio, decrease the average error, and significantly reduce the degree of deformation and artifacts.Second, utilizing the prior information plays a vital role in reconstructing high-quality images for limited-angle CT. However, the existing iterative methods do include priors inside the main iteration body, while initialization was overlooked. After such common initializations (zero image or FBP image), a large number of iterations are needed to produce relatively acceptable image and apparent artifacts nearby edges still can be noticed. To our knowledge, study on choosing optimal initial image for iterative reconstruction has not been published before. Therefore, how to get optimal initial image for limited-angle CT reconstruction is our priority in this work. In this work, we proposed to produce optimized initial image followed by total variation (TV) based iterative reconstruction by the feature of image symmetry. The proposed method contains four steps:first, reconstruct image by FBP algorithm; second, calculate and locate the symmetry axis of the object in the image; third, fill the region containing severe artifacts with artifact-free region in the image according to symmetry axis; fourth, the processed image in step third is used as initial image for projection on convex sets with total variation (POCS-TV) iterative algorithm to reconstruct CT images. The proposed method uses the image symmetry to eliminate the deformation artifacts and supply POCS-TV with a good initial image. Digital Shepp-Logan and real head phantoms are used to verify the feasibility of the proposed method. For simulation experiments and reconstruction of the real head phantom, compared with other initial images for POCS-TV, image by our method as initial image for POCS-TV can reconstruct high-quality image in which artifacts are effectively suppressed and edge structure information is better preserved.CT imaging as a subject involving mathematics, physics, medicine, computer science and other fields, has many factors affecting the imaging quality, such as different reconstruction methods, establishment of the physical model and the hardware support, etc. In this paper, the research is just a small branch of the limited angle CT imaging. Some preliminary achievements have obtained, but further study is needed in the future work.