  Speckle noise suppression is a challenging and crucial pre-processing stage
for higher-level image analysis. In this work, a new attempt has been made
using telegraph total variation equation and fuzzy set theory for speckle noise
suppression. The intuitionistic fuzzy divergence (IFD) function has been used
to distinguish between edges and noise. To the best of the author's knowledge,
most of the studies on multiplicative speckle noise removal process focus on
only diffusion-based filters, and little attention has been paid to the study
of fuzzy set theory. The proposed approach enjoy the benefits of both telegraph
total variation equation and fuzzy edge detector, which is not only robust to
noise but also preserves image structural details. Moreover, we establish the
existence and uniqueness of a weak solution of the regularized version of the
proposed model using Schauder fixed point theorem. With the proposed model,
despeckling is carried out on natural and Synthetic Aperture Radar (SAR)
images. The experimental results of the proposed model are reported, which
found better in terms of noise suppression and detail/edge preservation, with
respect to the existing approaches.
