Total variation restoration of speckled images using a split-bregman algorithm

Multiplicative noise models occur in the study of several coherent imaging systems, such as synthetic aperture radar and sonar, and ultrasound and laser imaging. This type of noise is also commonly referred to as speckle. Multiplicative noise introduces two additional layers of difficulties with respect to the popular Gaussian additive noise model: (1) the noise is multiplied by (rather than added to) the original image, and (2) the noise is not Gaussian, with Rayleigh and Gamma being commonly used densities. These two features of the multiplicative noise model preclude the direct application of state-of-the-art restoration methods, such as those based on the combination of total variation or wavelet-based regularization with a quadratic observation term. In this paper, we tackle these difficulties by: (1) using the common trick of converting the multiplicative model into an additive one by taking logarithms, and (2) adopting the recently proposed split Bregman approach to estimate the underlying image under total variation regularization. This approach is based on formulating a constrained problem equivalent to the original unconstrained one, which is then solved using Bregman iterations (equivalently, an augmented Lagrangian method). A set of experiments show that the proposed method yields state-of-the-art results.