Summary Ground penetrating radar (GPR) method is a non-destructive method for detecting shallow subsurface objectives based on the transmission of electromagnetic waves into the earth and the recording of received reflections from the sent waves. Noise recording of GPR data is inevitable. Noise attenuation is one of the most important and most significant steps in GPR processing. GPR data contains a variety of noise types. Random noise during data acquisition affects the quality of the data. Several noise reduction techniques have been proposed in various papers. In this paper, two methods of total variation (TV) and group sparsity total variation (GSTV) are used to reduce noise from GPR data in rational dilation wavelet transform (RADWT) and dual-tree rational dilation wavelet transform (DTRADWT) spaces. The TV method is an inversion method for noise attenuation of data. The developed type of TV is called GSTV. TV and GSTV methods are very effective in noise attenuation. However, due to the presence of random noise in all frequencies of the data, it is difficult to reduce noise in the data...