For any coherent imaging systems including ultrasound, synthetic aperture radar and optical laser, the multiplicative speckle noise degrades both the spatial and contrast resolution of the image. So, speckle suppression or despeckling is necessary before processing like image segmentation, edge detection, and in general any medical diagnosis. It is quite a mind-numbing task to analyze the corrupted images. Among many methods that have been proposed to perform this task either in spatial domain or in transformed domain, there exists a class of approaches that use coefficient modelling in transform domain. In this paper, we proposed a novel despeckling method in the nonsubsampled shearlet transform (NSST) domain with coefficient modelling. We used Bayesian maximum a posteriori (MAP) estimator with the priori assumption as heavy-tailed Lévy (HTL) distribution for estimating the noise-free NSST coefficients. Finally, experiments show that the proposed method outperforms others in terms of visual evaluation and image assessment parameters. Manuscript profile