Sparse Deterministic Deconvolution of Mars SHARAD Data

The Martian North Polar Layered Deposits (NPLD) are composed of layered ice and dust that record the changing climate over the last few million years. Shallow Radar (SHARAD) onboard the Mars Reconnaissance Orbiter (MRO) is critical for studying the fine structures and compositions of the NPLD. The radar reflectivity correlates to the changing properties of real stratigraphy (e.g.,dust content). Inversion of the reflectivity is commonly based on Fresnel equations, which is inefficient when coupling abundant subsurface reflectors such as those from NPLD. SHARAD data are considered as a convolution product of a known source wavelet and unknown sparse reflectivity series. Here, we propose a sparse deterministic deconvolution (SDD) method to obtain the NPLD reflectivity profile with enhanced resolution compared with raw radar data. We solve the reflectivity series as the
$\ell _{2}-\ell _{1}$
problem using a minimization technique by alternating direction method of multipliers (ADMM). Incoherent summing can be used to reduce speckle noise prior to deconvolution, leading to results with less impact from speckle noise. Synthetic and real data examples illustrate that the SDD method efficiently estimates subsurface reflectivity series and enables the detection of laterally continuous, subtle, and deep reflectors with higher resolution and sparsity. The proposed method provides a robust and efficient approach for inverting the reflectivity of SHARAD data, which is promising for investigating the detailed structure and composition of the polar caps that is related to Mars paleoclimate.