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Subsurface layers are preserved in polar regions on Mars, which are considered to be a record of past climate changes on Mars. Orbital radar instruments like the SHAllow RADar (SHARAD) on board Mars Reconnaissance Orbiter (MRO) transmit radar signals to Mars and receive a set of signals returned from interfaces having a contrast in dielectric properties in the probed subsurface regions. These subsurface layers which are preserved in the upper approximate to 1 km of the Martian Polar Layered Deposits (PLDs) can be observed in SHARAD radargrams. Extraction of these layering features is the preliminary work before interpreting and understanding their origins. In this study, we use a new method based on log-Gabor filtering and Continuous Wavelet Transform (CWT)-based peak detection to extract subsurface radar reflections and a workflow to remove clutter reflections in order to reconstruct 3-D subsurface layers. These methods and workflow are then tested on the SHARAD data in the Promethei Lingula region near the Martian south pole. The results show that following this workflow, the ground surface and six subsurface interfaces can be reconstructed, which aids in the interpretation of the depositional and erosional history of this region.