By Andrew T. Campbell
ISBN-10: 0738118117
ISBN-13: 9780738118116
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We remark that we should not consider the {b¯ l } (or b) at each frequency ω as an estimate of the ω-component of the missing data because other frequency components contribute to the residue term as well, which determines the covariance matrix Q (ω) in the APES model. 4 Initialization Since in general there is no guarantee that the EM algorithm will converge to a global maximum, the MAPES-EM algorithms may converge to a local maximum, which depends on the initial estimate θˆ 0 used. To demonstrate the robustness of our MAPES-EM algorithms to the choice of the initial estimate, we will simply let the initial estimate of α(ω) be given by the WFFT with the missing data samples set to zero.
01, two gaps involving 49 (40%) missing samples]. (a) True spectrum, (b) WFFT, (c) complete-data WFFT, (d) complete-data APES, (e) WFFT with interpolated data via GAPES, and (f ) GAPES. 2: Modulus of the 2-D spectra. (a) True spectrum, (b) 2-D data missing pattern, the black stripes indicate missing samples, (c) 2-D complete-data WFFT, (d) 2-D complete-data APES with a 2-D filter of size 16 × 25, (e) 2-D WFFT, and (f ) 2-D GAPES with an initial 2-D filter of size 10 × 8. 3: Modulus of the SAR images of the backhoe data obtained from a 48 × 48 data matrix with missing samples.
1 (10 dB higher than in the previous experiments). 01, 77 (60%) missing samples] obtained via. (a) WFFT, (b) GAPES with M = 64 and = 10−2 , (c) MAPES-EM1 with M = 64 and = 10−3 , and (d) MAPES-EM2 with M = 64 and = 10−3 . corresponding moduli of the spectral estimates of complete-data WFFT, APES, missing-data WFFT, GAPES, MAPES-EM1, and MAPES-EM2 are plotted in Figs. 6(f ), respectively. Again, the performance of the MAPES-EM algorithms is excellent. In our last experiment, we plot the RMSEs of the MAPES-EM1 estimates as functions of the missing sample rate in Fig.