A Variational Model for Removing Multiple Multiplicative Noises

Abstract

The problem of multiplicative noise removal has been widely studied in recent years. Many methods have been used to remove it, but the final results are not very excellent. The total variation regularization method to solve the problem of the noise removal can preserve edge well, but sometimes produces undesirable staircasing effect. In this paper, we propose a variational model to remove multiplicative noise. An alternative algorithm is employed to solve variational model minimization problem. Experimental results show that the proposed model can not only effectively remove Gamma noise, but also Rayleigh noise, as well as the staircasing effect is significantly reduced.

A Novel Fractional-Order Variational Approach for Image Restoration Based on Fuzzy Membership Degrees

“…The second term D(f, u) is the data fitting term that evaluates the distortion of the connection between u and the observation f and is derived from the MAP. We assume the noise model, based on the work in [25] and is modeled as follow.…”

“…Using the the logarithmic transform z = logu ⇐⇒ u = e z we can use the subsequent data fitting term along similar lines to Ref. [25] as…”

“…As far as we could remember, there are a few variational approaches concerned about the issue of multiplicative noise removal [19], [20]. For further details, the readers are referred to [21]- [25]. Fractional calculus is a fast developing mathematical subject, which gives a significant tool for non-local field theories and as such fractional-order PDEs based methods established to be a robust tool for image, signal, video, and optical fringe processing [26].…”