| Emission computed tomography（ECT）is a non-invasive molecular imaging technique.It is required to introduce a radiotracer into the human body,and obtain an estimate of the distribution of the tracer inside the human body by tomographic reconstruction of the detected emitted photons.For example,single-photon emission tomography（SPECT）plays an important role in the imaging diagnosis of diseases.The total variation regularization term is very effective in suppressing noise for medical image reconstruction,but the reconstruction results will produce a certain degree of staircase artifacts.In addition,it can only describe the image information in the horizontal and vertical directions,which is insufficient for image representation.Therefore,it is of great theoretical significance and practical value to explore regular terms that can suppress staircase artifacts and describe multiple directional information.Medical images have the characteristics of unclear boundaries,high noise,and insufficient contrast,so traditional wavelets have difficulties in characterizing their subtle differences.Multi-scale geometric analysis is a new signal analysis technology,which has been developed and applied in the fields of image compression,denoising,enhancement,and feature extraction,showing its strong development and application potential.Compared with the traditional wavelet transform,the multi-scale geometric analysis method is more in line with the visual effect of the human eye,can more effectively describe and capture the edge geometric features and rich details in the image,and can make full use of the geometric properties of the image itself to achieve better image quality.is a "sparse" representation.Therefore,this thesis studies the multi-scale geometric analysis method and its application in medical image reconstruction,aiming to explore new algorithms suitable for medical image reconstruction.The main work and contributions of the thesis are as follows:（1）Learn and introduce the theory of preprocessing alternating projection algorithm.In the second chapter,the establishment of the basic model is introduced,and then two regular terms are introduced.Finally,the preprocessing alternate projection algorithm for SPECT image reconstruction is introduced,which provides corresponding theoretical support for the subsequent model algorithm.（2）In-depth study of multi-scale geometric analysis methods.The third chapter of the thesis focuses on the basic theory,superior characteristics,and realization of curved waves,contour waves,and shear waves.The application of the product penalty term to SPECT image reconstruction research has laid a theoretical foundation.（3）In Chapter 4,a SPECT image reconstruction method based on a multi-scale geometric analysis method is proposed.Curvelet,contourlet,and shearlet are introduced to characterize the reconstructed image,and the Infimal convolution is used as the regular term of the reconstruction model,which is iteratively reconstructed by preprocessing alternating projections.Simulation experiments are designed to evaluate the reconstruction results of the algorithm under different noise levels and compare with the TV regularization term and ICTV regularization term.The experimental results show that the method in this thesis is better than the down-convolution total variation penalty term,which can further eliminate the staircase artifacts while suppressing the noise,and the edges and textures of the reconstructed images are clear,which is in line with the perceptual characteristics of the human visual system. |
