Digital Signal Processing Reference
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for example, higher resolution than APES, based on the (complete) data inter-
polated via MAPES. It is known that the rank-deficient robust Capon filter-bank
(RCF) spectral estimator [52] has higher resolution than the existing nonparametric
spectral estimators. Hence based on the data interpolated via MAPES-CM, we
apply rank-deficient RCF with a 20
20 filter-bank and a spherical steering vector
uncertainty set with unit radius. The resulting image is shown in Fig. 6.4(h), which
exhibits no sidelobe problem and retains all important features of Slicy. Compared
with Fig. 6.4(b), we note that although the data size was reduced from 288
×
×
288
to 32
32 and from the reduced data matrix 40% of the samples were omitted,
we can still obtain an image similar to that obtained by the WFFT applied to the
original high-resolution data. [Note that we cannot get a similar high-resolution
image with all the well-separated features and without sidelobe problem by simply
thresholding Fig. 6.4(f ), 6.4(g), or even 6.4(c).]
Next, we consider a 32
×
32 data matrix from the “Backhoe Data Dome,
Version 1.0.” At 0
◦
elevation, the data are collected from a 2
◦
azimuth cut centered
around 90
◦
azimuth, covering a 0.3 GHz bandwidth centered around 10 GHz.
Fig. 6.5(a) shows the WFFT image of the complete data matrix with smeared
features. Fig. 6.5(b) shows the APES image of the complete data with a 16
×
×
16
2-D filter. Some smeared features in Fig. 6.5(a) are clearly observed here, such as
the one located at row 26 and column 20. Fig. 6.5(c) illustrates the data missing
pattern, where the samples in row 5, 13, 14, 21, 22, 27 and in columns 8, 9, 10, 18,
19, 20, 26, 27 are missing. Figs 6.5(d) and 6.5(e) show the WFFT and MAPES-
CM images of the missing-data matrix. It can be observed that despite the missing
samples, MAPES-CM can still give a spectral estimate that has all the features
shown in Fig. 6.5(b).
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