Constrained Iterative Reconstruction by the Conjugate Gradient Method

The conjugate gradient method incorporating the object-extent constraint is applied to image reconstruction of a three-dimensional object using an incomplete projection-data set. The missing information is recovered by constraining the solution with the knowledge of the outer boundary of the object-extent which may be a priori measured or known. The algorithm is derived from the least-squares criterion as an advanced version of conventional iterative reconstruction algorithms such as SIRT (Simultaneous Iterative Reconstruction Technique) and ILST (Iterative Least Squares Technique). In the case of reconstruction from noisy projection data, a method based on the minimum mean-square error criterion is also proposed. Computer simulated reconstruction images of a phantom using limited angle and number of views are presented. The result shows that the conjugate gradient method incorporating the object-extent constraining provides the fastest convergence and the least error.