Existence Of Solutions For A Class Of Optimal Transportation Problems With Partial Information

In this paper,we study the existence of solutions for the optimal transportation problems with partial information in theory,and apply it to the inverse problem of signal processing in practice.As for construction of the paper,it is divided into four parts.At first,we introduce the background of optimal transportation and signal processing.Secondly,the optimal transportation problem in the background of spectrum estimation in signal processing is introduced,and the existence of the solution with partial information is proved by two methods.Thirdly,we introduce the optimal transportation problem in the background of Direction of arrival estimation(DoA)and localization in signal processing,and the existence of solutions for 2D or 3D uniform circular array with partial information is proved when certain conditions are satisfied.Finaly,the optimal transportation problem in spectrum estimation of signal processing is extended,unbalanced optimal transportation problem is considered,and the existence of the solution is proved.