  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.
