Variational-based speckle noise removal of SAR imagery

In this paper we present a variational method for synthetic aperture radar (SAR) speckle removal. Variational method is a newly developed technique for the removal of SAR´s multiplicative noise. For an image, we could define an energy functional. The energy evolves as the original image changes, and the minimum energy corresponds to the speckle reduced result. Partial differential equation (PDE) technique is used to get the minimal solution. Our energy functional makes use of the statistical information of the multiplicative noise since it follows a Gamma law with mean mu = 1 and variance sigma² = 1/M for M-look SAR. Our energy is a regularization term with two constraints. The regularization term is the integral for the norm of image gradient; two constraints are the mean of noise should be 1 and the variance of noise should be 1/M. We use the method of Lagrange multipliers, Euler-Lagrange equation and heat flow method to obtain the minimizer of the energy. ERS Precision Image (PRI) data are to demonstrate our algorithm. Numerical result shows that the speckle reduced image preserves edges and point targets while smoothes homogenous regions in the original image. The algorithm is computationally efficient and easy to implement.