Research On L₁ Regularization For X-ray Luminescence Computed Tomography

As a new molecular imaging technique, X-ray luminescence computed tomography (XLCT) has realized the early detection and diagnosis of the disease on the molecular and cellular levels by using nanophosphors as optical probe. However, because of the complexity of the transmission of light in biological tissues, the target reconstruction of XLCT is an ill-posed problem. Therefore, how to reconstruct the nanophosphors target is the core of the research on XLCT.In this paper, we focus on the two aspects of target reconstruction and algorithm evaluation for XLCT. We propose the new X-ray emission tomography reconstruction algorithm and improve the accuracy and efficiency of XLCT by obtaining accurate surface optical information. The main work is as follows:1) Sparse reconstruction by separable approximation sparse (SpaRSA) based on L1 regulation is introduced to solve the inverse problem. According to the theory of compressed sensing, the reconstruction of XLCT is considered as L1-regularized least squares (Ll-LS), which is transformed into a quadratic programming problem. In the numerical experiments and physical experiments, we compare the SpaRSA with the L1-LS algorithm. The experimental results show that the SpaRSA algorithm can obtain more quickly and accurate reconstruction results without using feasible region. In addition, the stability of SpaRSA is also verified by experiments with different noise, different optical parameters and different excitation times.2) For SpaRSA algorithm of target reconstruction accuracy is low when the nanophosphors target is located in the high depth, we introduce split augmented Lagrangian shrinkage algorithm (SALSA) based on L1 regularization. This algorithm splits single spatial variables into two variables mutually constrained. It gets their optimal approximate solutions alternately by the augmented Lagrangian method. Numerical experiments and physical experiments results show that, compared with the SpaRSA method, SALSA can effectively improve the accuracy of the reconstruction and the convergence speed. SALSA’s robustness is also verified by experiments on the noise, optical parametric mismatch and excitation frequency.3) In order to better evaluate the quality of X-ray luminescence computed tomography, we added three evaluation parameters in the reconstruction with SpaRSA and SALSA, including position error, relative error and normalized root mean square error. Each evaluation criterion can reflect the characteristics of the reconstructed image in some aspect.