Since Tian Jun proposed the difference expansion embedding technique,based on which,many reversible watermarking techniques were proposed.However,these methods do not perform well when the payload is high.In this pape...Since Tian Jun proposed the difference expansion embedding technique,based on which,many reversible watermarking techniques were proposed.However,these methods do not perform well when the payload is high.In this paper,we proposed an expandable difference threshold controlled scheme for these three methods.Experiments show that our scheme improves the performance of these three methods for heavy payload.展开更多
By using the Feynman-Kac formula and combining with Itˆo-Taylor expansion and finite difference approximation,we first develop an explicit third order onestep method for solving decoupled forward backward stochastic d...By using the Feynman-Kac formula and combining with Itˆo-Taylor expansion and finite difference approximation,we first develop an explicit third order onestep method for solving decoupled forward backward stochastic differential equations.Then based on the third order one,an explicit fourth order method is further proposed.Several numerical tests are also presented to illustrate the stability and high order accuracy of the proposed methods.展开更多
基金the National High Technology Research and Development Program (863) of China (No.2007AA02Z452) the National Natural Science Foundation of China (Nos.30570511 and 30770589)
文摘Since Tian Jun proposed the difference expansion embedding technique,based on which,many reversible watermarking techniques were proposed.However,these methods do not perform well when the payload is high.In this paper,we proposed an expandable difference threshold controlled scheme for these three methods.Experiments show that our scheme improves the performance of these three methods for heavy payload.
基金supported by the NSF of China(No.12001539)the NSF of Hunan Province(No.2020JJ5647)China Postdoctoral Science Foundation(No.2019TQ0073).
文摘By using the Feynman-Kac formula and combining with Itˆo-Taylor expansion and finite difference approximation,we first develop an explicit third order onestep method for solving decoupled forward backward stochastic differential equations.Then based on the third order one,an explicit fourth order method is further proposed.Several numerical tests are also presented to illustrate the stability and high order accuracy of the proposed methods.
