Research On Filtered Backprojection Algorithms Of CT Image Reconstruction

Computerized Tomography (CT) is a technology that obtains the tomogram of the observed objects. It is widely used in many scientific domains such as medical diagnosis , radio astronomy, electron micrology and radar. Its applications in medical diagnosis are arresting especially. CT, which obtains a series of projection data of objects concerned from several viewing angles, can get the tomograms of the objects through the technology of image reconstruction. The transform methods, especially the filtered or convolution backprojection algorithms are widely used in the commercial CT systems. This thesis explores and researches the algorithms of the backprojection under this research background.Because of the inherent complex number operation characteristics of the Fourier transform algorithm in computation, the reconstruction algorithm based on it, will bring some problems such as increasing the complexity of the mathematic processing, will need more memory space and slowing down the computation speed. However, the projection data and the object functions they all belong to the real number area in applications of CT image reconstruction. Hartley transform is a sinusoidal transform similar to Fourier transform. Fast Hartley transform can be achieved by using the structures similar to that in Fast Fourier transform. Hartley transform has three advantages over Fourier transform. It is a real number transform and has the same forward and inverse transform formulas. Besides that, it needs less internal storage than Fourier transform. Hence, using Hartley transform in many real signal and real data processing can avoid the use of complex arithmetic so as to reduce the numbers of arithmetic operations and improve the computational efficiency. This thesis realizes the filtered backprojection algorithms of CT image reconstruction by using Hartley transform. It shows that we can use Hartley transform instead of Fourier transform in fields of the image reconstruction. The numbers of arithmetic operations and the internal storage needed in image reconstruction algorithms based on Hartley transform are almost half as much as that in Fourier transform while retaining the precision.Based on the geometrical relationships between image pixels and projection rays...