Convergence criterion for MBIR based on the local noise-power spectrum: Theory and implementation in a framework for accelerated 3D image reconstruction with a morphological pyramid.

Model-based iterative reconstruction (MBIR) offers improved noise-resolution tradeoffs and artifact reduction in cone-beam CT compared to analytical reconstruction, but carries increased computational burden. An important consideration in minimizing computation time is reliable selection of the stopping criterion to perform the minimum number of iterations required to obtain the desired image quality. Most MBIR methods rely on a fixed number of iterations or relative metrics on image or cost-function evolution, and it would be desirable to use metrics that are more representative of the underlying image properties. A second front for reduction of computation time is the use of acceleration techniques (e.g. subsets or momentum). However, most of these techniques do not strictly guarantee convergence of the resulting MBIR method. A data-dependent analytical model of noise-power spectrum (NPS) for penalized weighted least squares (PWLS) reconstruction is proposed as an absolute metric of image properties for the fully converged volume. Distance to convergence is estimated as the root mean squared error (RMSE) between the estimated NPS and an NPS measured on a uniform region of interest (ROI) in the evolving volume. Iterations are stopped when the RMSE falls below a threshold directly related with the properties of the target image. Further acceleration was achieved by combining the spectral stopping criterion with a morphological pyramid (mPyr) in which the minimization of the PWLS cost-function is divided in a cascade of stages. The algorithm parameters (voxel size in this work) change between stages to achieve faster evolution in early stages, and a final stage with the target parameters to guarantee convergence. Transition between stages is governed by the spectral stopping criterion. The approach was evaluated on simulated CBCT data of a realistic digital abdomen phantom. Accuracy of the NPS model and evolution with time of the distance from the measured NPS was assessed in two ROIs. Performance of the spectrally-driven mPyr architecture was compared to a conventional, single stage, PWLS, and to two mPyr designs running a fixed number of iterations. The spectrally-driven mPyr achieved faster convergence, with 40% lower RMSE than the single stage PWLS, and between 10% and 20% RMSE reduction compared to other mPyr designs. The proposed spectral stopping criterion proved to be a suitable choice for a stopping rule, and, in particular, to govern mPyr stage transition.