Reduced memory augmented Lagrangian algorithm for 3D iterative x-ray CT image reconstruction

Although statistical image reconstruction methods for X-ray CT can provide improved image quality at reduced patient doses, computation times for 3D axial and helical CT are a challenge. Rapidly converging algorithms are needed for practical use. Augmented Lagrangian methods based on variable splitting recently have been found to be effective for image denoising and deblurring applications.5 These methods are particularly effective for non-smooth regularizers such as total variation or those involving the 1 norm. However, when standard "split Bregman" methods6 are applied directly to 3D X-ray CT problems, numerous auxiliary variables are needed, leading to undesirably high memory requirements.7 For minimizing regularized, weighted least-squares (WLS) cost functions, we propose a new splitting approach for CT, based on the alternating direction method of multipliers (ADMM)1,5 that has multiple benefits over previous methods: (i) reduced memory requirements, (ii) effective preconditioning using modified ramp/cone filters, (iii) accommodating very general regularizers including edge-preserving roughness penalties, total variation methods, and sparsifying transforms like wavelets. Numerical results show that the proposed algorithm converges rapidly, and that the cone filter is particularly effective for accelerating convergence.