Synthetic aperture radar image and its despeckling using variational methods: A Review of recent trends

•SAR provides 2D high-resolution images, making it a valuable tool for remote sensing.•Recent SAR systems better perceive dynamic processes due to higher mapping abilities.•SAR images are hampered by speckle noise, making data interpretation challenging.•Despeckling research trend has grown from basic filtering to advanced deep learning.•The variational methods are reviewed by stating their usage, benefits, and drawbacks. Synthetic aperture radar (SAR) has drawn significant interest from the remote sensing community due to its ability to provide high-resolution images irrespective of weather and illumination conditions. It has numerous applications in a variety of fields, including military surveillance, geological exploration, disaster management, and mapping of natural phenomena like climate change, forest management, and volcanic eruptions. The image acquired by coherent sensors such as SAR is corrupted by granular multiplicative noise, also known as speckle. It has an adverse influence on the visual interpretation of SAR images and prevents the use of various post-processing tasks. Despeckling addresses the removal of such noise from SAR images while preserving the image details. This work provides a brief summary of the theory, applications, speckle statistics, performance measures, and recent developments in despeckling filters using variational methods for SAR images. The primary focus is given to recently proposed despeckling filters, discussing their typical usage, benefits, and drawbacks.