Sparse non-convex L-p regularization for cone-beam X-ray luminescence computed tomography

Cone-beam X-ray luminescence computed tomography (CB-XLCT) is an attractive hybrid imaging modality, and it has the potential of monitoring the metabolic processes of nanophosphors-based drugs in vivo. However, the XLCT imaging suffers from a severe ill-posed problem. In this work, a sparse nonconvex L-p (0 < p < 1) regularization was utilized for the efficient reconstruction for early detection of small tumour in CB-XLCT imaging. Specifically, we transformed the non-convex optimization problem into an iteratively reweighted scheme based on the L-1 regularization. Further, an iteratively reweighted split augmented lagrangian shrinkage algorithm (IRW_SALSA-L-p) was proposed to efficiently solve the non-convex L-p (0 < p < 1) model. We studied eight different non-convex p-values (1/16, 1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8) in both 3D digital mouse experiments and in vivo experiments. The results demonstrate that the proposed non-convex methods outperform L-2 and L-1 regularization in accurately recovering sparse targets in CB-XLCT. And among all the non-convex p-values, our L-p(1/4 < p < 1/2) methods give the best performance.