Speckle noise corrupt the major part of ultrasound image, because of which the quality deteriorate and loss of valuable information leads to false diagnosis. A large community of images like synthetic aperture radar (SAR) image, Synthetic image, and simulated ultrasound image, require despeckling at pre-processing stage for better processing. Cleaning the speckle from image and preserving the edge details is a vital task. Nowadays not only despeckling is considered as an important process but also preserving information at boundary and edges of image is also important. As most of the algorithms able to remove speckle noise but fails to preserve the details of edges. This paper covers several recent methods for removal of speckle noise along with various metrics opted for comparisons. The distinctive part of this paper is, a mathematical and parametric review has been done. Also a table is also included which summarizes the entire paper.