Studies Of The Block-iterative Algorithm For Image Reconstruction

The two most important image reconstruction methods are analytic algorithm and iterative algorithm .Landweber's iterative algorithm is an important method based on the iterative algorithm. In this article we study the relaxation parameter's selection in the Landweber's block-iterative algorithms. We select the special relaxation parameter and put the projection matrix into many blocks according to the projection angles in the reconstruction procedure, and reconstruct the image according to the form we get the projection data strictly. We select the product ofλand one ratio the maximal eigenvalues of the multiples of the block-matrixes and their conjugate transpose matrixes as the special relaxation parameters .By performing numerical experiment ,we conclude that ifλapproach to 1/6-1/7, we will get the best result when we can obtain the complete datum.; Otherwise, that we select the special relaxation parameter and put the projection matrix into many blocks according to the projection angles is available to the limited angle problem. In this article, we have certified the possibility of the above by performing the concrete numerical experiment. Furthermore, we have founded that on condition that the size of the image and the number of the lines at each of projection angle are certain, we can make the average error smaller by reducing theλproperly when the number of the projection angles increase gradually or increasing theλwhen the number of the projection angles decrease.