Issue 50

A. Kostina et alii, Frattura ed Integrità Strutturale, 50 (2019) 667-683; DOI: 10.3221/IGF-ESIS.50.57 679 Savitzky-Golay and median filtering. The brief description of each method is given below. For each of the considered techniques the optimal parameters providing maximum value of SNR had been obtained by exhaustive search method . (a) (b) Figure 13 : Effect of the coating thickness on reconstructed contrast (1 – reconstructed signal, 2 – reference signal, 3 – initial signal with noise): (a) results obtained with the use of true depth (b) results obtained with the use of false depth. The reference signal and corrupted signal correspond to the data presented in Fig. 11 (a) for all applied filtration techniques. The simple moving average method is the most popular technique due to its simplicity. In equation form, it can be written as [22]:          1 0 1 M k C i z i k M (22) where    C is the output signal,    z is the input signal, M is the number of points in average. Results of filtration obtained with the optimal value of  14 M are presented in Fig. 14 (a). Processing of the input signal by Gaussian filter can be described using convolution [23]:               1 0 M k C i z i M k g k (23) where  M is the kernel shift which is typically equal to the half-width of the kernel M (      1 2 1 M M ),    g is the kernel. A normalized Gaussian kernel is defined as:                                 2 2 1 2 2 0 exp exp 2 2 M l k M l M g k   (24) where 2  is the variance,   0, 1 k M . Application of the Gaussian filtering with the optimal values of M =15 and  =12 which provide the highest value of SNR for this filtration technique is demonstrated in Fig. 14 (b). The basic idea of the Savitzky-Golay filtration technique is to fit input data set by polynomials of some degree [24-25]. Coefficients of polynomials should provide the minimal mean-square error n e :           2 M n n M e p n z n (25) where M is the half-width of the approximation interval,      0 N k k k p n a n is the polynomial of the N th degree, k a is polynomial coefficients.