Research On Reconstruction Algorithms Of CT With Incomplete Projection Data

Reconstruction from incomplete data for CT results from part of projection data which are unable to be measured. Incomplete data problems occur quite frequently because of practical constraints due to the imaging hardware, scanning geometry, and ionizing radiation exposure, etc. The incomplete data problem may take many forms. For example, one type of the incomplete data problem derives from attempting to reconstruct an image from projection data at few views. Another example of an imperfect scanning data situation comprises limited angular range of the object to be imaged. still another example comprises gaps in the projection data caused by bad detector bins, etc. Researches on reconstruction from incomplete data have significantly meaning. For example, the incomplete data cause by reducing radiation Dose for patient and induced by metal implants in patients, etc. In recent years, there have been intensive interests on reconstruction from incomplete data.The projection data are not sufficient for exact reconstruction for topographic images and application of traditional algorithms, such as filtered back projection, may lead to conspicuous artifacts in reconstructed images. While iterative reconstruction method performs well. Although the huge load of computation prevent it from application in CT image reconstruction. Due to recent advances in parallel computing and computer technology, the iterative reconstruction method may prove to be practicable and become hot research area. In this dissertation, we mainly concern about on improving algebraic iterative method in the application of reconstruction with incomplete projection data.For ART (algebraic reconstruction technique), keeping an eye on the projection sequence in traditional Algebraic Reconstruction Technique, a modified algorithm is proposed. The proposed algorithm does projection in an order which is decided by the value of pseudo error of each hyperplane computed from initial guess solution in prior. This motivation comes from consideration of deviation from correct position for hyperplanes results from ill-posed model of CT image reconstruction. Furthermore, another proposed algorithm adjust the projection sequence in the same way except that making the obtained solution in the last iteration as new initial guess to compute the pseudo error. Experimental results indicate that both modified algorithm give much better results than the classical one.Simultaneous Iterative Reconstruction technique is another important algebraic iterative algorithm, the update term adopted during iterative procedure is computed from all of projection rays, and amends the imprecise solution caused by error of projection measurement of single ray. After focus analysis of different kind of algorithm of simultaneous iterative reconstruction technique, such as Cimmino's algorithm, Landweber algorithm, SART, CAV and DROP, a general formula of SIRT is concluded. Based on Cimmino's algorithm, an improved algorithm is proposed. Traditional algorithm over depend on the system matrix during iterative procedure and error of system matrix lead to inaccurate solution, The proposed algorithm introduces the last iterative solution to the weighted operator in backprojection procedure, aiming to approximate entries of system matrix, thus becomes robust under the error system matrix. We implement the modified algorithm in an ordered subset manner and achieve better results than traditional algorithms after mid term of the iterative procedure.We show that the Twomey's nonlinear iterative algorithm for inverting aerosol size distribution data in material subject or measurement research field can be used to computerized topographic image reconstruction. This mainly because of both reconstructions belongs to the solution of equations of the first kind of Fredholm. To our acknowledgement, there's no report on adopting Twomey's algorithm in CT image reconstruction. We introduce this algorithm in CT image reconstruction. Numerical experiments indicate that the Twomey's algorithm gives good results.In the last part of this dissertation, the proposed and introduced algorithms have been tested under benchmark of some cases of CT image reconstruction from incomplete projection data. Cases include half detectors problem under parallel beam and limited angle problem under fan beam geometry. Moreover, in the case of limited angle problem, we discuss the selection strategy of the projection angle and make a conclusion that for aim of reducing radiation dose and promoting scanning speed, one should make sure that the scan angle is not less than the smallest angle (short scan range) needed for reconstruction of accurate image. Other strategy such as selecting scanning angle less than short scan range and increasing ray sums at the same time is not practicable since it can improve reconstruction image in a limited extent even adopting more rays in such scanning range and results to increasing the radiation dose.