Regularization Based Reconstruction Algorithms For Bioluminesccnce Tomography

Small animal imaging is an indispensable technical tool in preclinical biomedicalresearch which relies on the use of animal models to understand human disease. As anewly emerging optical molecular imaging techniques, bioluminescence tomography(BLT) offer an inexpensive and sensitive alternative to more established imagingtechnologies. It allows for non-invasively imaging a variety of physiological andpathological activities at cellular and molecular levels in living small animals，and thusit is expected to be a very promising tool in disease diagnosis, therapy monitor and drugdevelopment.The aim of BLT is to reconstruct the3D distribution of the internalbioluminescence sources from limited measurements on the external surface. Afterseveral years of continuous research, the imaging theory of bioluminescencetomography has been preliminarily established. Nevertheless, in order to obtain stableand meaningful results with reasonable computation cost, reconstruction algorithms forBLT have to address two crucial issues, the inherent ill-posedness of the inverseproblem and the large scale of numerical problems involved in tomography for complexanimal models. Because of insufficient surface measurement and highly diffusive natureof the photon propagation through biological tissues，most existing reconstructionalgorithms suffer from several limitations in the aspects of detecting depth,reconstruction accuracy, and computation efficiency, which prevent the BLT techniquefrom reaching it full potential in practical preclinical research.According to the imaging difficulty and demands in practical utilization, this thesisfocuses on exploring specific methods based on regularization technique for solvingBLT inverse problem, practical regularization parameter choice schemes, fastreconstruction algorithms for whole-domain BLT, and reconstruction strategies forimages quality improvement. The main research work includes:1) In view of that geometric errors caused by discretization or acquisition ofanatomical structures in BLT as well as measurement noises will affect the finalreconstruction result, a reconstruction algorithm based on truncated total leastsquares method (TTLS) is developed to deal with a variety of system noise andmeasurement noise. Moreover, based on the modified generalized cross validation(GCV) criterion and minimization of residual error, a hybrid parameter choicescheme named HGCV is developed for determining optimal truncation level in TTLS. The proposed reconstruction algorithm can deal with various errors causedby model discretization, acquisition of anatomical structures, determination ofoptical parameters and external measurement together, which is different from thepresent algorithms used in BLT that only consider measurement noise. Thenumerical simulations demonstrate the effectiveness and robustness of TTLScombined with HGCV for solving BLT inverse problem.2) A reconstruction algorithm named as stage-wise fast LASSO (SwF-LASSO) isproposed for whole domain BLT, which does not rely on a priori knowledge suchas permissible source region or multispectral boundary measurements. Thismethod takes full advantage of the sparseness of the source distribution in mostscenarios of BLT applications, and the boundary measurement is significantlyinsufficient. Therefore, the goal of bioluminescence source reconstruction can beregarded as finding sparse solutions from large underdetermined systems of linearequations, which is essentially the same as that of compressive sensing tasks. Bysparse regularization, we reformulated the BLT inverse model to an l1minimization problem and developed a novel reconstruction algorithm based onfast sparse approximation scheme for least squares support vector machine, whichcan fulfill whole domain fast reconstruction iteratively. Numerical experimentalresults on a heterogeneous mouse atlas evaluate the efficiency and accuracy of theproposed method, as well as the multiple sources resolution. In vivo mouseexperimental reveals that it can achieve high computational efficiency and accuratelocalization of source, which further indicate its potential for a practical BLTsystem.3) As for the problem of accurate detecting different sources that differ greatly indensity or power, we build a unified regularization framework for multiple sourcesreconstruction by integrating an iterative multiple source detection strategy (MSDS)with the general lp-norm regularization. Rather than assuming independencebetween mesh nodes, the proposed reconstruction strategy exploits spatial structureof nodes and aggregation feature of density distribution on the finite element meshto adaptively determine the number of sources and to improve the quality ofreconstructed images. An appealing property of this framework is its flexibility.The MSDS is a relatively independent component of the regularization framework,and hence different regularizers and different reconstruction algorithms can beutilized according to the practice of BLT. Numerical simulations and phantomexperiments demonstrate the effectiveness of this framework. 4) As in many other imaging modalities, the computational challenge in BLT is toreach the desirable resolution within acceptable computational cost. We present ahybrid multilevel reconstruction scheme by combining the ability of sparseregularization with the advantage of adaptive finite element method. In contrast tothe previous AFEM based BLT in the literature，the proposed method take thecharacteristics of different discretization levels into account, and two differentinversion techniques are employed on the initial coarse mesh and the succeedingones to maintain solution stability and computational economy. The hybrid AFEMbased reconstruction does not require either permissible source region constraint ormulti-spectral measurements. Moreover, by providing fine resolution aroundtargets with coarser resolution in other region, it reaches a compromise betweencomputational precision and efficiency under the precondition of desirableresolution. Numerical experiment results with a digital mouse model demonstratethat the proposed scheme can accurately localize and quantify source distribution.