Research Of Ultrasonic Computed Tomography Based On The Ray Theory

Ultrasonic computed tomography(UCT) transmits ultrasound waves through an object by transmitting probes, and obtains ultrasound measurements such as travel-times by receiving probes. Based on the measurements, cross-sectional images which show the spatial distribution of the physical components of the object can be acquired without damaging the material. Ultrasound offers several advantages: noninvasiveness, nonionizing radiation, harmless to human, and cheap to produce. The UCT has been broadly applied to various fields such as geophysics, biomedical engineering and industrial flaw detection etc.UCT based on ray theory is composed of two parts, the forward problem solved with the velocity model to obtain traced ray paths, the inverse problem solved with real ray travel-times and traced ray paths to obtain the latest velocity model. At present, UCT has three disadvantages: first, most of methods just use the projection data to reconstruct, without using the prior knowledge of the material, leading to a low spatial resolution of UCT image; second, in existing iterative reconstruction algorithms, the velocities of background area and defective areas do disturb each other with the error distribution strategy which divides error evenly among cells; third, in existing iterative reconstruction algorithms, it needs to carry out a forward process after each error correction step, resulting in a long running time, since the forward process need to consider all of the possible ray paths.In this dissertation, we focus on the application of industrial flaw detection via UCT, in which the material to be detected is often a collection of a background area and a small amount of defective areas. We reconstruct the ultrasonic velocity model of material using the sparse priors of material. The Matching Pursuit(MP) is utilized to greedily search defect cells one by one to find out the velocity model that most closely matches the projection data. Simultaneously, we also study the ray tracing algorithm based on the boundary linear traveltime interpolation in order to increase the calculating precision and reduce calculating time. The main content is as follows.1) The traditional linear traveltime interpolation(LTI) algorithm is based on linear assumption, while the rays through multiple grids will lead to error accumulation. In order to reduce the cumulative errors in this application, a new ray tracing algorithm is proposed based on the boundary linear traveltime interpolation. Our algorithm inserts nodes on the boundary of different areas to determine the ray refractional angle. By making use of multidirectional loop computation minimum traveltimes of all grid points, which will conform the traced ray path to the condition of minimum traveltimes when rays transported from the reverse direction. The simulation results show that the proposed algorithm is better than the traditional LTI algorithm and the cross-scanning LTI algorithm for computing traveltime, tracing path and the algorithm running time.2) In the applications of industrial flaw detection via UCT, where background areas and defect areas to be reconstructed are often centralized. Since UCT is an underdetermined problem, meanwhile most of reconstructed images have local smooth characteristics; we can exploit prior knowledge of the material sunch as gradient sparsity and discrete cosine transform(DCT) domain sparsity to constrain the solution space for a good reconstruction result. We propose a new composite model based on SIRT for reconstruction of UCT, which combines gradient sparsity and DCT sparsity, the former corresponds to total variation(TV) norm term and the later corresponds to DCT L0 norm term. Furthermore, we solve this problem based on fast composite splitting technique. Compared with traditional SIRT algorithm, the imaging reconstruction combing prior knowledge of the original signals gives improved results, with clearer image outline and more precise defective areas.3) Iterative ultrasonic computed tomography(UCT) based on ray theory uses the initial straight line paths to iterate that will lead to error diffusion. Since the defect areas are sparse when compared to the background area, we can borrow the idea of matching pursuit(MP) algorithm in Compressed Sensing(CS) to greedily search the defects. An effective two-step algorithm is developed to reduce the cumulative error in the image reconstruction. In the first step, a threshold-based method is designed to roughly distinguish defect fuzzy area from background area according to the differences between measured ray travel-times and calculated ray travel-times. In the second step, the Matching Pursuit(MP) is utilized to search defect cells more accurately. Furthermore, in each iteration boundary linear travel-time interpolation, a new algorithm proposed by us, is applied as the forward algorithm to further reduce the cumulative error and the amount of calculation. Simulated results show that the proposed algorithm outperforms the method: LTI+SIRT.4) In the above method based on MP, defect cells are searched out one by one, however, the search could be slow when the search area is large. The backtracking-based matching pursuit(BMP) method is utilized to reconstruct the sizes and positions of defective areas in order to speed up the search process. The BMP method first chooses several cells as defective cells at each time, and then uses a backtracking strategy to remove some cells chosen wrongly in t he processi ng, to i dentif y t he support set more accuratel y. The effecti veness of t he propose d method is exa mi ned by simulated results.