Studies of the Relaxation Parameter Selection of the Block-iterative Algorithm for Image Reconstruction

Landweber's iterative algorithm is an important method in the image reconstruction.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.We select the product ofλand one ratio the maximal eigenvalues of the multiples of the block-matrixes (specified later) 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.