Investigation Of Reconstruction Algorithms For Incomplete CT Projections

As an important nondestructive testing (NDT) technology, computed tomography(CT) can obtain the external and internal structure characteristics of the object from2Dor3D images by using the X-ray projection data from multiple projection views. It hasbeen widely used in medical diagnosis, industrial flaw detection, reverse engineering,airport security, restoration of cultural relics and other fields as its advantages ofnondestructive, high precision and3D visualization. In order to obtain accuratereconstruction images, using conventional analytic reconstruction algorithm oftenrequires complete projection data. However, in some practical applications, restricted byscanning environment or scanned object, the projection data obtained is incomplete.Reconstruction problem from incomplete projection data means that the images arereconstructed by using the projection data which do not satisfy the exact reconstructionconditions. To get high quality CT image reconstructed by incomplete projection data isa challenging work. How to make use of incomplete projection data to reconstruct highquality CT image has not only important academic value but also important applicationvalue, which is always the focus of research.In medical diagnosis, it has great significance to reduce the risk of high radiationdose imposed to the patients, thus reducing the patient radiation dose has beenresearched a lot. Because the patient radiation dose is proportional to the number ofX-ray projections, controlling the CT system for sparse sampling of X-ray projectionviews is an effective technology to reduce the patient radiation dose. In recent years, thetotal difference minimization (TDM) regularized iterative reconstruction algorithm hasobtained good performance for few-view CT. However, the total difference (TD)-basedregularization just considers the sparsity of the gradient, thus, the protection of the edgestructure information of the object is slightly insufficient. To effectively reduce thepatient radiation dose and improve the quality of reconstruction image, we present aniterative reconstruction algorithm based on weighted total difference (WTD)minimization. The WTD measure not only enforces the gradient sparsity, but alsoenforces the gradient continuity, thus it can effectively protect the edge information indifferent direction. The experimental results indicate that WTD-based reconstructionalgorithm achieves better performance in terms of suppressing streak artifacts andpreserving the edge structure information of the object, and can effectively improve the quality of the image reconstructed.In some practical applications of CT imaging, restricted by the scanningenvironment and the scanned objects etc., X-ray can only penetrate into objects at alimited angular range. In these cases, scanning angular range cannot even achieve exactreconstruction condition knows as short scan conditions (such as180plus fan angle),thus, it will lead to limited angle problem for CT image reconstruction. Significantstreak artifacts and gradual changed artifacts nearby edges are present in reconstructedimages by conventional analytical reconstruction algorithm (such as FBP algorithm). Inindustrial applications of CT testing, the scanned industrial parts often consists of asingle or several kinds of materials, and the same material has the same or approximateattenuation coefficient. Thus, the CT image is approximately piecewise-constant(Piecewise Constant), and the gradient image is sparse. Based on the sparsity of thegradient image, total variation minimization (TVM) based iterative reconstructionalgorithm has been widely used. The image reconstruction based on TVM cansignificantly reduce streak artifacts in few-view CT, but it suffers from the gradualchanged artifacts nearby edges. To suppress this kind of artifacts, we investigate animage reconstruction model based on l0gradient minimization for limited-angle CT.Unlike TVM reconstruction algorithm, the l0norm of the image gradient is taken as theregularization function in the proposed reconstruction model. Regularization of the l0norm of the image gradient can globally control the variations of gradient amplitude,thus, it can effectively protect the edge and suppress the noise. To effectively solve thereconstruction model, we transformed the optimization problem into a few optimizationsub-problems and then, solved these sub-problems in the manner of alternating iteration.The experimental results based on simulated and real projection data indicate that theproposed algorithm can effectively suppress the streak artifacts and the gradual changedartifacts nearby edges simultaneously.In industrial applications, crack or defect detection of industrial parts is animportant goal in nondestructive testing and nondestructive evaluation. In some cases,X-ray cannot effectively penetrate the object only in a limited scanning angular range.Thus, the projection data in these scanning angular range cannot effectively reflect theattenuation degree of X-ray passing through objects. Using the projection data in thesescanning angular range, the image reconstructed by conventional analyticalreconstruction algorithm suffers obvious metal artifacts. The metal artifacts willseriously interfere with the evaluation for nondestructive testing. When the image is reconstructed not using the projection data in these scanning angular range, it will leadto limited angle CT. Since the advantages of TV regularized iterative reconstructionalgorithm for limited angle CT, this article will apply this algorithm to reduce metalartifacts. Considering projection data corresponding air can accurately locate thecontour of the object, when combined with TVM based algorithm, making full use ofthe projection data that corresponding to the air in the direction that X-ray cannotpenetrate the object, can effectively remove the metal artifacts caused by X-ray notpenetrating the object. The experimental results verify the effectiveness of the schemeused.The health monitoring of pipeline in service (such as detection of the oil pipeline inservice) plays an important role in preventing the happening of the disaster andeconomic loss reduction. Since the helical scanning trajectory can satisfy the conditionof exact reconstruction and with the aid of slip ring technology, helical cone beam CThas been widely used in the medical area. Restricted by testing environment and theblockade of slip ring technology, helical cone beam CT scanning trajectory directly usedfor nondestructive testing of the pipeline in service has significant limitations. Sincethere is a high degree of freedom of C-arm, a variety of complex trajectories for3Dimaging can be achieved. In this paper, we study an X-ray CT scanning imaging modelusing C-arm, called limited-angle inverse helical cone-beam CT. In this mode, theangular range of the cone beam X-ray scanning around the pipeline in service does notexceed180°(such as120°), and scanning process is finished in the absence of slip-ringtechnology. Due to the motion trajectory of X-ray source does not satisfy exactreconstruction condition, it will lead to limited angle CT. In this paper, we will applyTVM based iterative reconstruction algorithm to the new scanning imaging model. Theexperimental results show that the regularized reconstruction algorithm based on TVMcan suppress the artifacts and noise in the new scanning imaging mode, and improve thequality of reconstruction image.Since linear scan cone beam CT is a technically simple CT configuration and easyto realize, it can be used for long objects inspection. In this scanning mode, X-raysource and detector do linear motion relative to the detected object, and each point inthe detected object can only be covered in the limited scanning angular range bycone-beam X-ray, thus, it will lead to limited angle CT. While applying the TVM basediterative reconstruction algorithm to the linear scan cone beam CT reconstruction, theimage reconstructed is blurry and distorted near the edges of the object. To overcome this drawback, we generalize the2D piecewise constant modification algorithm to3Dcase, and apply the3D algorithm to the linear scan cone beam CT reconstruction. In theprocess of correction, we first use3D C-V image segmentation algorithm to locate theedge of the image reconstructed, and then, get the corresponding sub-region accordingto the edge of the detected by using region growing method, finally, substitute averagegray intensity value for the gray intensity values of all voxels in each sub-region. Thus,it makes images consisted of piecewise constant regions. By introducing the3Dpiecewise constant modification algorithm into the TVM based iterative reconstructionalgorithm, we gain a new algorithm called piecewise constant modification based TVMreconstruction algorithm (PCM-TVM). The experimental results show that PCM-TVMalgorithm can reduce artifacts caused by TVM based reconstruction algorithm, andmake the edges of the object clearer and more accurate.