A Hybrid Regularizer Combining Orthonormal Wavelets and Finite Differences for Statistical Reconstruction in 3-D CT

Statistical reconstruction methods for X-ray CT rely on regularization to yield good quality images. We propose and investigate a specific type of nonquadratic regularization for 3-D CT reconstruction that corresponds to applying a 2-D orthonormal wavelet transform (OWT) on trans-axial slices and finite differences (FD) along the axial direction. We use an iterative variable-splitting-based alternating direction method of multipliers (ADMM) reconstruction algorithm that effectively handles the proposed regularizer. We also present a simple procedure to incorporate iteration-dependent random shifting to circumvent the shift-variance of OWT and to reduce block artifacts. The proposed regularizer requires less memory compared to those that use FDs and is thus advantageous for ADMM that stores and manipulates auxiliary variables related to the regularizer. We demonstrate using simulation with a 3-D XCAT phantom that the proposed regularizer yields images that are visually comparable in quality to those obtained using a regularizer composed of FDs.