中文摘要：

针对分子成像领域中的反源问题,利用Tikhonov正则化方法,构造了一种通过求解一个极小化问题来重构源函数的新方法.利用目标泛函的严格凸性等性质,证明了极小化问题解的存在惟一性.由有限元方法的误差估计及细致分析,证明了离散化后极小化问题解的收敛性和误差估计,并通过数值实验验证了该方法的有效性.

英文摘要：

A new method was proposed for the inverse source problem of the molecular imaging by solving a certain minimization problem though Tikhonov regularization method.The unique existence of the solution for the minimization problem is ensured by strict convexity of the objective functional.The convergence property and error estimate of the finite element solution for the discrete minimization problem were also discussed.The computational performance of our new method was shown by several numerical tests.