A functional minimization interpretation of fast iterative reconstruction algorithms

The functional minimization framework is used to show that the quadratic algorithm gains its advantage by substituting an estimate of D^-1 which is refined at each estimate for the differing, but static, estimates used by most competing methods. This observation identifies the quadratic algorithm as one of the class of quasi-Newton procedures. Empirical convergence comparisons are provided for several linear algorithms, the quadratic and cubic algorithms, and the conjugate gradient algorithm for various inputs x and operators D. The results clearly show the superior convergence of the polynomial algorithms over both the local gradient and conjugate gradient methods