Fast iterative reconstruction in X-ray tomography using polar coordinates

We aim at reducing the high memory need and the long reconstruction time of the iterative methods for reconstructing the X-ray tomography images. In general, iterative methods are capable of providing a higher quality reconstructed image compared to those obtained through filtered backprojection. This is because in the iterative methods, a more accurate model is used in the reconstruction process. The model used in this technique accounts for the noise and can incorporate some prior knowledge on the image and therefore can provide images with higher quality compared to those obtained using the filtered backprojection technique. The reconstruction problem can then be solved using optimization techniques.;In using iterative methods for image reconstruction, the large size of the projection matrix is the main cause of having high memory need in this method. Moreover, requiring to perform projection and backprojection operations numerous times is the main reason for the long reconstruction time. These problems need to be addressed properly for wider adoption of the iterative approaches in image reconstruction.;The work presented herein aims at addressing these problems by developing an efficient technique which makes reconstruction of clinical size images possible. This will be done in a simple framework under the assumption of a monochromatic X-ray source. The objective is fulfilled by considering the fact that the geometry of commercial tomographs is invariant in polar coordinates. Using polar coordinates for representing the object, the coefficients of the projection matrix will be highly redundant. The matrix is also very sparse and has a block-circulant structure. Consequently, using polar coordinates for representing the object leads to a significant decrease in memory requirement. There are some questions associated with this type of representation which include numerical efficiency of the reconstruction process using this type of representation and actual quality of reconstructed image. This work tries to study and address these questions.;As already mentioned, reconstruction time of tomography problems is mainly determined by the computation time of projection and backprojection operations that need to be performed at each iteration. The parallel implementation of these operations can reduce the reconstruction time significantly and is addressed here. Moreover, by designing preconditioners tailored to the structure of the objective function a sufficient increase in the convergence speed of iterative methods was achieved.;The current work is a preliminary study on the efficiency of using polar coordinates for representing the object and reconstructing the tomography images. The results which have been obtained in this work can now be used for developing the 3D reconstruction of clinical data.;We can also use the developed algorithms in this work to expand the current framework to.;polychromatic model and benefit from the efficiency of this model in reducing the metal artifacts.