Ground penetrating radar clutter removal via randomized low rank and sparse decomposition for missing data case

Dealing with ground penetrating radar (GPR) data with missing entries can affect the performance of clutter removal methods heavily, making target imaging/detection via GPR practically impossible. This paper proposes a two-step approach based on the matrix completion property of the randomized low rank and sparse decomposition called Go Decomposition (GoDec). The first step of the proposed method recovers the missing samples via matrix completion. The resulting low-rank part corresponds to the recovered version, with sparse part fixed as an indicator matrix for the missing entry locations and corrupted GPR data as input. The second step is a straightforward implementation of the low rank and sparse decomposition to the recovered image, giving the clutter and target components as low and sparse parts of the decomposition. Comparisons with conventional methods and recent methods such as robust principal component analysis (RPCA) and one-step GoDec demonstrate that the proposed method recovers the target image for missing data case where all the other methods fail. Although GoDec remains slightly behind RPCA for uncorrupted data, the proposed two–step GoDec (TS-GoDec) outperforms them for missing data. The peak signal-to-noise ratio (PSNR) values reached by TS-GoDec are better than its closest follower RPCA around 42% in average. Since GoDec is very fast, TS-GoDec method still remains faster than RPCA which presents poorer results for the missing data case.