Local tomography property of residual minimization reconstruction with planar integral data

Residual minimization with the well-known conjugate gradient (CG) algorithm has been applied to medical image reconstruction for years. The main advantage of this method is its fast convergence rate. In this paper, we point out that this method has another property-local tomography, when this image reconstruction method is applied to planar integral projections. By local tomography we mean the following: The object is relatively large, the entire object is not sufficiently measured, and the projections are truncated due to a small detector size. However, a small region-of-interest (ROI) is sufficiently measured. The small ROI is able to be exactly reconstructed. This local tomographic property is found for planar integral data only and is not found for line-integral measurements. Iterative local tomography has been applied to cosα/r weighted planar integral data through computer simulations and phantom experiments. An efficient projector that models the cosα/r weighting factor is also developed.