Study On X-ray CT Reconstruction Algorithm For Insufficient Projection Data

Since the discovery of X-ray,it has been widely used in the field of imaging science.The properties of short wavelength and high penetration make X-ray filling the gap between optical microscope and electron microscope.In recent years,with the improving of X-ray source performance and introduction of synchrotron radiation experiment apparatus and micro-nano-optical components of the processing technology improving,the X-ray nanometer CT technology has been developed significantly.X-ray nano-CT can be divided into soft X-ray nano-CT and hard X-ray nano-CT.Soft X-ray nano-CT due to the existence of "water window" has natural contrast for biological samples.So it can image without additional staining of samples,thus it has widely used in biological mechanisms,drug research,environmental and other fields.Because of its strong penetration and large focal depth,the hard X-ray nano-CT is very suitable for materials sample lossless in situ detection.So it has been widely used in materials science,energy,microelectronics and other fields.The nano-CT system first collects the two-dimensional projection information of the sample.In order to obtain the accurate and clear three-dimensional structure of the sample,the three-dimensional reconstruction process is needed.Good quality of reconstruction get more accurate reflection of the three-dimensional structure information of the sample,also is the basis for follow-up research.However,due to the influence of the equipment,samples and experimental conditions,the actual X-ray CT process is difficult to obtain a complete sample projection data.For incomplete projection data,the result of traditional reconstruction algorithm is often not ideal,limiting the application and development of X-ray CT.The main contributions of this thesis are described as follows:1.This paper summarizes the development of X-ray imaging and the development of CT equipment.This paper introduces the main optical elements and the synchrotron radiation source in the process of X-ray CT development into the nanometer stage,and introduces the soft X-ray nano-CT and hard X-ray nano-CT working principle and the application field.Several typical examples were selected to show the advantages and application value of X-ray nano-CT.At the same time,we also analyze the current problems faced by X-ray nano-CT,including:few-view projection angle,limited projection angle,noise projection data,and the causes of these problems.2.The basic principles of CT imaging are researched,including the generation process of projection and the different imaging methods,and the Fourier Central Slice theorem in CT reconstruction.The traditional transform reconstruction algorithm and the algebraic reconstruction algorithm have been compared.And we analyze the advantages and disadvantages of different traditional algorithms,and reconstruct and compare them with incomplete projection data.3.The new equally sloped reconstruction algorithm and the total variation reconstruction algorithm are studied,and its application are briefly introduced.After analyzing the characteristics of the new algorithms,in order to make up for deficiencies of equal sloped algorithm,we propose a modified equally sloped algorithm based on the total variation algorithm.Through the comparison of the results of a large number of simulation experiments,the values of the parameters in the modified algorithm are determined.4.In order to verify the performance of the modified algorithm,we conducted a series of simulation experiments,including:few-view projection angle,limited projection angle,noise projection data and comprehensive situation.We compared the performance of the filtering back projection algorithm,the equal sloped reconstruction algorithm and the modified algorithm,and found that the improved algorithm is the best reconstruction algorithm.In addition,we also compare the reconstruction time of these algorithms and investigate their iterative convergence process.5.According to the characteristics of the soft X-ray nano-CT in National Synchrotron Radiation Laboratory,we selected hydroxyapatite and yeast cells for soft X-ray computed tomography,and reconstruct the image and render the result.At the same time,in order to confirm the performance of our improved algorithm,we also show the excellent performance of the modified algorithm by calculating the diameter of hydroxyapatite and divide the different organelles of yeast cells.It provides a new method for the reconstruction of nano-CT.