Applications of wavelet analysis in differential propagation phase shift data de-noising

Abstract

Using numerical simulation data of the forward differential propagation shift (ϕDP) of polarimetric radar, the principle and performing steps of noise reduction by wavelet analysis are introduced in detail. Profiting from the multiscale analysis, various types of noises can be identified according to their characteristics in different scales, and suppressed in different resolutions by a penalty threshold strategy through which a fixed threshold value is applied, a default threshold strategy through which the threshold value is determined by the noise intensity, or a ϕDP penalty threshold strategy through which a special value is designed for ϕDP de-noising. Then, a hard-or soft-threshold function, depending on the de-noising purpose, is selected to reconstruct the signal. Combining the three noise suppression strategies and the two signal reconstruction functions, and without loss of generality, two schemes are presented to verify the de-noising effect by dbN wavelets: (1) the penalty threshold strategy with the soft threshold function scheme (PSS); (2) the ϕDP penalty threshold strategy with the soft threshold function scheme (PPSS). Furthermore, the wavelet de-noising is compared with the mean, median, Kalman, and finite impulse response (FIR) methods with simulation data and two actual cases. The results suggest that both of the two schemes perform well, especially when ϕDP data are simultaneously polluted by various scales and types of noises. A slight difference is that the PSS method can retain more detail, and the PPSS can smooth the signal more successfully.