A Variational Model to Remove the Multiplicative Noise in Ultrasound Images

In this paper we study a variational model to deal with the speckle noise in ultrasound images. We prove the existence and uniqueness of the minimizer for the variational problem, and derive the existence and uniqueness of weak solutions for the associated evolution equation. Furthermore, we show that the solution of the evolution equation converges weakly in BV and strongly in L2 to the minimizer as t→∞. Finally, some numerical results illustrate the effectiveness of the proposed model for multiplicative noise removal.

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