l_q稀疏正则化理论及其在热传导反问题中的应用  

l_q sparsity regularization theory with the application to a backward heat conduction problem

作　　者：赵光伟[1] 

机构地区：[1]哈尔滨商业大学能源与建筑工程学院,哈尔滨150028

出　　处：《黑龙江大学自然科学学报》2014年第6期752-756,共5页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(11301119)

摘　　要：lq(0<q≤1)稀疏正则化在实际应用领域已经得到了广泛的应用。在信号处理领域,简单的迭代算法能够得到满意的重构结果,但是,针对较为复杂的偏微分方程反演问题,利用这些算法进行反演往往很难达到最佳的重构效果。将已有的迭代算法进行改进,并将其应用到热传导反演问题中,通过和标准的吉洪诺夫正则化方法进行比较,说明lq稀疏正则化方法和改进的迭代算法的优点。l^q （0 〈 q ≤ 1 ） sparsity regularization has been widely applied in real fields. In signal processing field, the plausible reconstruction can be obtained by using a simply iterative algorithm. However, the good reconstruction is difficult to be obtained by using a simply iterative algorithm in complex inverse problems for partial differential equations. Hence, the existing iterative algorithm is improved, and the new method is applied to a backward heat conduction problem. By comparing with a standard Tikhonov regularization, the advantages of an lq sparsity regularization and an improved iterative algorithm are obtained.

关 键 词：反问题 稀疏正则化 逆热传导问题 迭代算法 

分 类 号：O241.8[理学—计算数学]