Adaptive sparse modeling and shifted-poisson likelihood based approach for low-dosect image reconstruction

Recent research in computed tomographic imaging has focused on developing techniques that enable reduction of the X-ray radiation dose without loss of quality of the reconstructed images or volumes. While penalized weighted-least squares (PWLS) approaches have been popular for CT image reconstruction, their performance degrades for very low dose levels due to the inaccuracy of the underlying WLS statistical model. We propose a new formulation for low-dose CT image reconstruction based on a shifted-Poisson model based likelihood function and a data-adaptive regularizer using the sparsifying transform model for images. The sparsifying transform is pre-learned from a dataset of patches extracted from CT images. The nonconvex cost function of the proposed penalized-likelihood reconstruction with sparsifying transforms regularizer (PL-ST) is optimized by alternating between a sparse coding step and an image update step. The image update step deploys a series of convex quadratic majorizers that are optimized using a relaxed linearized augmented Lagrangian method with ordered-subsets, reducing the number of (expensive) forward and backward projection operations. Numerical experiments show that for low dose levels, the proposed data-driven PL-ST approach outperforms prior methods employing a nonadaptive edge-preserving regularizer. PL-ST also outperforms prior PWLS-ST approach at very low X-ray doses.