Provably convergent coordinate descent in statistical tomographic reconstruction

Abstract

Statistical tomographic reconstruction algorithms generally require the efficient optimization of a functional. An algorithm known as iterative coordinate descent with Newton-Raphson updates (ICD/NR) has been shown to be much more computationally efficient than indirect optimization approaches based on the EM algorithm. However, while the ICD/NR algorithm has experimentally been shown to converge stably, no theoretical proof of convergence is known. We prove that a modified algorithm, which we call ICD functional substitution (ICD/FS), has guaranteed global convergence in addition to the computational efficiency of the ICD/NR. The ICD/FS method works by approximating the log likelihood at each pixel by an alternative quadratic functional. Experimental results show that the convergence speed of the globally convergent algorithm is nearly identical to that of ICD/NR.