Medical CT Image Reconstruction Based On Framework Of Lambda Tomography

It is the first time that slice imaging derived from computed tomography (CT) is used widely with huge breakthrough. Today, CT is one of the most important part in radiodiagnosis which is a mature and accepted method in clinic. It is reinforce or replace the traditional X-ray tomography in many aspects.CT was developed with a high rate in 1970s, and then growed in a very lazy rate without any material achievements in 1980s. Therefore, people considered that CT was less important along with the appearance of magnetic resonance (MR). On the contrary, CT is in the peak of development and reexpanding its territory of applications. The development of helical CT and the transformation form single slice scanning to the fast volume scanning are the two main reasons of making the CT re-attracted. The applications of multi slice detector system and sub-second scanning time are the tops of CT development in technique and clinic.Why did the slice images have a higher contrast? A contrast of an image is defined as the intensity difference of two neighboring pixels or regions. The contrast of slice image was contributed directly by the value of attenuation between the neighboring voxels, but not contributed by the line integral calculated through the whole human body. The contrast was decided by the local tissues directly. The neighboring tissues or overlapped tissues would not or less affect it. Therefore, whether the density of tissue or the random tiny difference of component, we could display them with adequate contrast in principle. What the CT displayed was the value of attenuation of pixel distributed by the corresponding voxel. It is easy to identify the focus because the contrast of CT images was contributed by the local difference of attenuation. In this case, people expect to reconstruct the CT image with high quality.Reconstruction for CT image is interesting and complicated. Since 1970s and 1980s, the researches for this field has been developed tremendously with the advancement on clinical CT scanner. A lot of methods were proposed and we had to make balance and compromise among computed complexity, spiral resolution, time resolution, noise, clinical therapy scheme, agility and artifacts. The object that we try to reconstruct can be considered as a two-dimensional distribution of some kind of function. For CT, this function represents the linear attenuation coefficients of the object. The problem imposed on the tomographic reconstruction can be stated as the following. Suppose we have collected a set of measurements. Each measurement represents the summation or line integral of the attenuation coefficients of an object along a particular ray path. These measurements are collected along different angles and different distances from the iso-center. To avoid redundancy in the data sampling, let us assume that the measunrements are taken in the following sequence. We first take a set of measurements along paths that are parallel to each other and are uniformly spaced. These measurements form a "view" of a "projection". We repet the same measurement process at a slightly different angle. This process continues to cover the entire 360 deg (theoreticallym only 180 deg of parallel projection are necessary). During the entire process, the angular increment between adjacent views remains constant and the scanned object remains stationary at the same location. The question of CT reconstruction is , how do we estimate the attenuation distribution of the scanned object based on these measurements?Because the ionizing radiation may induce cancers and genetic damage in the patients during CT scanning, it is highly desirable to develop an imaging algorithm for X-ray scan. As one of the local imaging techniques, the Lambda imaging reduces the X-ray dose and imaging time.Comparing with the filtered backprojection (FBP) algorithm based on Pi-line, lambda tomography (LT) can also exactly reconstruct an object from fanb-eam data using the two-dimensional Calderon operator. Its result possessed high contrast since the noises were amplified when we were enhancing the edges of the object. But there are first derivatives and second derivatives existing in the reconstruction formula of LT, which are sensitive to the noises. Apparently, we are not satisfied with these results. On the other hand, the three-dimensional Calderon operator can not exactly reconstruct an object for the three-dimensional cone-beam reconstruction.First, we proposed to introduce the Gaussian.kernel function to rebuild the projection data to avoid the derivatives sensitive to the noises. We also analyzed how to choose the parameters of the Gaussian kernel function. Second, We proposed a novel reconstruction method from cone-beam based on the FDK (Feldkamp-Daivs-Kress). FDK-type method should be faster than the Pi-line based algorithm in the case of scanning smaller volume object or bigger ROI. That is because the general LT algorithm contained the process of how to choose the Pi-line while it cost plenty of time. Also, we introduced the three-dimensional Gaussian kernel function convoluting with the projection data acquired from the pseudo-LT (PLT) to build a new projection data, which enhanced the ability of robusting to the noises. A lot of experiments are also provided to prove the validity of the models and their corresponding approaches mentioned in the paper.