Computed Tomography (CT) is a technique that obtains inner two-dimensional (2D) cross-sectional or three-dimensional (3D) structural images of an object using multiple X-ray measurements (projections) taken at different angles around the scanned object. It can show the interior structures, defects and material components of the inspected object with a nondestructive, distinct and accurate manner. And it has been widely used in many domains such as diagnosis medicine, manufacturing industry, military and security check etc., which is considered as one of the best modern nondestructive technique. For cone-beam X-ray CT, the scanned objected is rotated around the rotation center (or the X-ray source and planar detector are rotated around the scanned object), the cone shaped X-ray beam can cover a section of the inspected object at each view angle and collect the attenuated X-ray signals by planar detector to obtain the projection data, then, reconstruction algorithm is used to reconstruct the 3D inner image of the scanned section of the object. Compared with 2D CT, Cone-beam CT, acquired data by use of high density planar detector, can shorten the scanning time and make use of the x-ray more effectively, and the longitude resolution of the reconstruction image is higher. It can obtain more than thousand images with one turn scanning. Helical cone-beam CT not only has the merits of cone-beam CT but also can solve the problem of detecting long object such as humans, pipelines etc. as a natural way, and the scanning loci satisfy the conditions for exact reconstruction. With the developments of manufacturing technology of planar detectors, the improvements of the radiation resistance and anti-disturbance performance in flat-panel detectors, planar detector-based cone-beam CT made a breakthrough in CT imaging in terms of large 3D volume reconstruction and isotropic resolution, and it is gradually used to industrial CT which is one development direction of industrial CT.Using the same detector size of traditional full-covered CT, the helical cone-beam CT scanning based on field of view (FOV) half-covered can almost double the FOV, whose mechanism is simple and the scanning efficiency is the same as that of traditional helical cone-beam CT. During reconstruction, the extended helical cone-beam FDK algorithm (called half-covered helical FDK for short) is developed. There is no need for rebinning and interpolation of the projection data of this algorithm, so it can avoid the error from rebinning and interpolation. Compared with full-cover helical cone-beam CT, it only takes approximately half of the time for reconstruction as that of standard helical cone-beam FDK algorithm. So the computational efficiency of this algorithm is high. Only a little more than a half cross-section of an object needs to be illuminated with x-rays at every view angle, and the projection data of the half-cover helical cone-beam CT is transverse, but the ramp filter is non-local, so the reconstruction image has truncation error. Regarding this problem, this paper extends the idea of 2D local reconstruction to 3D half-covered helical cone-beam CT, and develops an improved half-covered helical cone-beam CT reconstruction algorithm based on localized reconstruction filter. Experimental results indicate that the presented algorithm well solves the truncation error of the half-covered helical FDK algorithm, improves the quality of the reconstruction image. And for the noise projection data, the presented algorithm can suppress noise and get better results. Moreover, the reconstruction time is much less.Owing to the limitation of on-the-scene inspecting conditions (for instance, the inspection of in-service pipeline, the pipeline is too near to ground or there are some other pipelines or objects next to the inspected pipeline to hinder the inspection etc.) or consideration of the X-ray radiation dosage and the scanning time, sometime the rotation angle of cone-beam can't reach the required minimum angle for reconstruction (for example, the required minimum angle of circular FDK algorithm is PI plus horizontal cone-angle ), then, it will occur the limited angle cone-beam CT. When the diameter of scanned object is too large or the central iron material can't be penetrated by X-ray, and the outer is our interesting part (such as pipelines etc.), then it can offset the detector and let the cone shaped X-ray beam only covering the outer part of the scanned object, and under this condition, it will occur the exterior cone-beam CT. The limited angle and exterior cone-beam CT are two typically truncated reconstruction problems and have significant meanings in practical applications. One industrial part (or one human organ) is always consist of one kind or several kinds of materials, the same material of casting (or the same tissue of human body) has identical or similar attenuation coefficient. So, the CT image is approximately piecewise-constant(except the grayscales of some images are gradual) and its gradient image is sparse which conforms with the assumption of compressed sensing. In recent years, as the application of CS in CT reconstruction, the total variation minimization (TVM) based regularization iterative reconstruction algorithms have achieved approval results for few-views problems. These algorithms are also effective for limited angle cone-beam problems, except there are still gradually changed artifacts in the nearby regions of contours. And the TVM based algorithms are used to exterior cone-beam CT which only can obtain reconstructed images with blurred and distorted contours. For the drawback of TVM based algorithms to limited angle cone-beam problems, in this paper, the 2D slide correction algorithm is generalized to the case of 3D. And by introducing the 3D slide correction method into the TVM regularization algorithms, we get a new iterative algorithm for limited angle cone-beam CT, which is referred to as cone-beam slide-corrected TVM (CBSC-TVM). For the drawback of TVM based algorithms to pipe-like objects exterior cone-beam problems, and in order to improving the quality of reconstructed image, the 2D subregion averaged correction algorithm which is based on 2D C-V (Chan-Vese) model, is generalized to 3D case to obtain a 3D C-V model based 3D subregion averaged correction algorithm. In the process of correction, it divides the 3D preliminary reconstruction image into some subregions by using 3D C-V active contours model, and then averages the grayscale values of all voxels in each subregion respectively. By introducing the 3D subregion averaged correction method into the TVM regularization algorithm, we get a new algorithm for exterior cone-beam problem, which is referred to as cone-beam subregion-averaged TVM (CBSA-TVM). Experiment results verify that CBSC-TVM to limited angle cone-beam CT and CBSA-TVM to exterior cone-beam CT can improve the quality of reconstructed images.In some practical applications of CT, detecting contours (or edges) of different contrast image regions of scanned object are the essential and necessary requirements, and high-quality imaging is not necessary to achieve the final goal of detecting and characterizing objects within the reconstructed images. For instance, in industrial applications, including image segmentation and object defect recognition and measurement, and industrial CT based inverse design which obtain the computer aided design (CAD) graph used in industrial manufacturing; in medicine applications, detection and highlighting of boundaries of organs, tissues, focus regions (such as tumors) are also the essential and necessary requirements. The main stream method is a two-step process, the image is reconstructed from projections first, and then it is followed by an edge detection operation on the reconstructed image. This method is time-consuming and post-processing of a reconstructed image is often difficult(because any practical CT projection data more or less have some noises, and even when the noise in the projection is white, the noise in the reconstructed image always may be nonwhite). For the application requirement of nondestructive testing and the drawback of the two-step method, on the basis of studying the relationship of wavelet and its Radon transform projection, and using back-projecting method for constructing 3D non-tensor product wavelet and its application to image edge detection, an algorithm for reconstructing object contours directly from helical cone-beam projections based on wavelet analysis and single-slice rebinning (SSRB) method is presented. Experiment results show the usefulness and high efficiency of the presented algorithm. For some cases of noisy projection data, the edge detection outcome by our algorithm is obvious better than that of two-step approach. Moreover, the run-time is much less than that of two-step approach. |