Compressed Sensing-Based Reconstruction For Bioluminescence Tomography

In recent years, bioluminescence tomography (BLT) has been widely studied as apromising optical molecular imaging technique due to its significant advantages in highspecificity, sensitivity, safety and cost effectiveness high signal-to-noise ratio (SNR).Bioluminescence tomography has been applied in the animal experiments andpreclinical trials of gene expression, tumor detection and drug development, etc. Nowthe research of bioluminescence tomography focus on the forward model and theinverse reconstruction of the light source. As an early imaging modality, the source ofBLT has a sparse distribution and the optical signals obtained by the imaging equipmentfrom the surface of the animal are weak. Meanwhile because the transmission of photonis complex, the inverse reconstruction of the BLT light source is a severely ill-posedproblem as an underdetermined linear equation in mathematics. Based on thecompressed sensing theory and the sparsity of bioluminescent source distribution, thedissertation conducts the inverse reconstruction problem. The author’s majorcontributions are outlined as follows:1. A three-dimensional bioluminescence tomography reconstruction algorithm isproposed based on primal-dual interior-point method. In order to reduce the severelyill-posedness of the BLT inverse problem, we propose a primal-dual interior-point(PDIP) method based on the compressed sensing theory and the sparsity ofbioluminescent source distribution. The PDIP method takes the l1norm problem as aminimization problem of linear programming. In order to obtain the optimal solution ofthe minimization problem, the Karush-Kuhn-Tucker condition is used to restrain thesolving process. Using the Newton method, we obtain the optimal solution to theprimal-dual equation. Reconstruction results on numerical simulation validate theaccuracy and effectiveness of the proposed method. Then in vivo mouse experimentvalidate the feasibility of the proposed method in early detection of clinicaloncology.2. A three-dimensional bioluminescence tomography reconstruction algorithm isproposed based on weighted iterative shrinkage/thresholding algorithm (WISTA). Insome computational studies, l1regularization methods are often less sparse than lp(0<p<1) regularization methods. We take the inverse problem as a lp(0<p<1) normminimization problem and propose a high-efficiency lp(0<p<1) regularization methodsto solve the minimization problem based on the iterative shrinkage/thresholdingalgorithm. The regularization method does not need of priori information about the permissible source region or multispectral data. Through the comparison betweenWISTA and other l1and l2regularization methods, the algorithm is proved to be moresparser and have better reconstruction results by numerical simulation of a3D mouseatlas. The last in vivo mouse experiment demonstrates that WISTA could be applied inpractical application.3. A comparison of six regularization methods is conducted through a series ofexperiments to study various conditions that affect the inverse BLT reconstruction. Theregularization methods have become the mainstream strategy to obtain the optimalsolution of the BLT inverse problem. But there is no generally accepted method whichcan be suitable for all of the reconstruction cases. We intend to fill the gap in theexisting studies to systematically benchmark the performance of thelp-regularization-based BLT reconstruction algorithms. In order to investigate theresponses of these algorithms to the permissible source region, measurement noise,optical properties and tissue specificity, we conduct a series of single source numericalphantom experiments. Then, the double sources numerical phantom experiment and thein vivo mouse experiment are carried out to further test their performances. For mostexperiments, the lp(0<p<=1) regularization algorithms achieve better reconstructionresults than l2regularization. In the four lp(0<p<=1) regularization algorithms, IVTCGand WISTA are generally more effective than the other two methods.4. A three-dimensional bioluminescence tomography reconstruction algorithm isproposed based on weighted interior-point algorithm (WIPA). In recent years, many l1regularization methods have been researched for various of inverse reconstructionproblem. However, the sparse property of the l1regularizer is often less than that of l0regularizer in many practical applications. In order to find more sparse solutions thanthe l1regularizer, many lp(0<p<1) regularization methods have been proposed to solvethe minimization problem. Based on the l1/2regularizer, the weighted interior-pointalgorithm converts BLT object function to weighted l1regularization problem andobtains the inverse reconstruction solution by interior-point algorithm. The3Dnumerical experiments demonstrate the effectiveness of the WIPA.