Cone-Beam Algebraic Reconstruction Using Edge-Preserving Regularization

This paper describes an algebraic algorithm for volume reconstruction from cone-beam projections. Since this is an ill-posed problem, regularization is necessary. While standard regularization methods are based on a smoothness assumption, we propose a regularizing process which preserves the reconstructed object edges. This method involves the minimization of a non quadratic energy criterion, difficult to solve, which we transform into a half-quadratic dual energy system, simple to minimize. Moreover, we have used two approaches to reduce the reconstruction time: storage of the non-null elements of the projection matrix and restriction of the reconstruction to the region of support. This method is developed for thyroid pinhole emission imaging. We present some results on a thyroid simulation and on a thyroid phantom using single circular orbit acquisition geometry. This method runs on conventional workstations within acceptable times. This regularized algebraic method gives high quality results and can be used in clinical practice.