Nonconvex sparse regularizer based speckle noise removal

This paper focuses on the problem of speckle noise removal. A new variational model is proposed for this task. In the model, a nonconvex regularizer rather than the classical convex total variation is used to preserve edges/details of images. The advantage of the nonconvex regularizer is pointed out in the sparse framework. In order to solve the model, a new fast iteration algorithm is designed. In the algorithm, to overcome the disadvantage of the nonconvexity of the model, both the augmented Lagrange multiplier method and the iteratively reweighted method are introduced to resolve the original nonconvex problem into several convex ones. From the algorithm, we can obtain restored images as well as edge indicator of the images. Comprehensive experiments are conducted to measure the performance of the algorithm in terms of visual evaluation and a variety of quantitative indices for the task of speckle noise removal.

► We present a new variational model for speckle noise removal.
► A nonconvex regularizer rather than the total variation is used to preserve edges of an image.
► The advantage of the nonconvex regularizer is pointed out in the sparse framework.
► The augmented Lagrange multiplier method and the iteratively reweighted method are introduced to solve our model.
► Both a denoised image and an edge indicator are obtained from the algorithm.