Statistical X-ray CT reconstruction using a splitting-based iterative algorithm with orthonormal wavelets

Regularized image reconstruction methods are of increasing interest for X-ray CT imaging, but are hampered by the long computation times of iterative algorithms. We recently developed a variable splitting-based alternating direction method of multipliers (ADMM) that provides superior convergence speeds for statistical X-ray CT reconstruction compared to conventional methods. ADMM however demands storing auxiliary constraint variables and can become memory-expensive when shift-invariant regularization operators (e.g., finite differences) are used, especially in 3-D CT. Since an orthonormal wavelet transform (OWT) is memory-efficient, in this work, we employ OWT with nonquadratic regularization in ADMM for CT reconstruction. We propose a practical strategy for performing iteration-dependent random shifting in ADMM to (partially) compensate for the shift-variance of OWT and reduce block-artifacts therefrom. Preliminary evaluations with a 2-D synthetic phantom and real 2-D in-vivo human head data indicate that the proposed strategy provides CT reconstructions that are comparable in quality to those obtained using nonquadratic regularization with finite differences.