SCIENCE CHINA Information Sciences, Volume 61, Issue 4: 042302(2018) https://doi.org/10.1007/s11432-016-9068-y

## Baseline distribution optimization and missing data completionin wavelet-based CS-TomoSAR

Hui BI1,2,*,
• AcceptedMar 23, 2017
• PublishedAug 25, 2017
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### Abstract

In this paper, we propose a coherence of measurement matrix-basedbaseline distribution optimization criterion, together with an ${L_1}$regularization missing data completion method for unobserved baselines(not belonging to the actual baseline distribution), to facilitatewavelet-based compressive sensing-tomographic synthetic aperture radarimaging (CS-TomoSAR) in forested areas. Using $M$ actual baselines, wefirst estimate the optimal baseline distribution with $N$ baselines$(N > M)$, including $N-M$ unobserved baselines, via the proposedcoherence criterion. We then use the geometric relationship between theactual and unobserved baseline distributions to reconstruct thetransformation matrix by solving an ${L_1}$ regularization problem, andcalculate the unobserved baseline data using the measurements of actualbaselines and the estimated transformation matrix. Finally, we exploitthe wavelet-based CS technique to reconstruct the elevation via thecompleted data of $N$ baselines. Compared to results obtained using onlythe data of actual baselines, the recovered image based on the datasetobtained by our proposed method shows higher elevation recovery accuracyand better super-resolution ability. Experimental results based onsimulated and real data validated the effectiveness of the proposed method.

• Figure 1

Recovered normalized elevation profiles based on data from observed actual baseline distribution ${{\boldsymbol{B}}_M}= \left[0, 15, 28, 44, 60, 75, 91, 100\right]$ with $M = 8$ (Blue) and estimated optimal virtual baseline distribution ${{\boldsymbol{B}}_N}$ with $N = 15$ (Red). Two scattering areas with different intensities are used to simulate the elevation distribution in the forested area (Black). The SNRs of the simulated echo data are (a) $\infty$, (b) $5 {\kern 3pt}{\rm dB}$, (c) $0 {\kern 3pt}{\rm dB}$, and (d) $-5 {\kern 3pt}{\rm dB}$, respectively.

• Figure 2

Estimated elevations (in meters) of two scattering centers with identical distribution of scattering areas (representing ground and canopy) under increasing distances between two centers. The true positions are represented by a horizontal line referring to the ground and a diagonal line referring to the scattering center of the canopy at varying elevations. Estimated elevations based on the data of (Upper) observed actual baseline distribution ${{\boldsymbol{B}}_M}$, (Lower) estimated optimal virtual baseline distribution ${{\boldsymbol{B}}_N}$ with $N = 15$. From left to right column in each row: the SNRs equal $0 {\kern 3pt}{\rm dB}$, $5 {\kern 3pt} {\rm dB}$, and $\infty$, respectively. (Black dots: two centers detected. Red dots: one center detected.)

• Figure 3

Tomogram span as a function of range and elevation using a 21-by-21 window based on the real airborne dataset. Recovered results based on (a) actual six L-band 2D focused SAR complex image data using the conventional beamforing method, (b) actual six L-band 2D focused SAR complex image data using the wavelet-based CS method, and (c) the completed dataset of ten estimated optimal virtual baseline distribution using the wavelet-based CS method.

• Figure 1

Recovered normalized elevation profiles based on data from observed actual baseline distribution ${{\boldsymbol{B}}_M}=~\left[0,~15,~28,~44,~60,~75,~91,~100\right]$ with $M~=~8$ (Blue) and estimated optimal virtual baseline distribution ${{\boldsymbol{B}}_N}$ with $N~=~15$ (Red). Two scattering areas with different intensities are used to simulate the elevation distribution in the forested area (Black). The SNRs of the simulated echo data are (a) $\infty$, (b) $5~{\kern~3pt}{\rm~dB}$, (c) $0~{\kern~3pt}{\rm~dB}$, and (d) $-5~{\kern~3pt}{\rm~dB}$, respectively.

• Figure 2

Estimated elevations (in meters) of two scattering centers with identical distribution of scattering areas (representing ground and canopy) under increasing distances between two centers. The true positions are represented by a horizontal line referring to the ground and a diagonal line referring to the scattering center of the canopy at varying elevations. Estimated elevations based on the data of (Upper) observed actual baseline distribution ${{\boldsymbol{B}}_M}$, (Lower) estimated optimal virtual baseline distribution ${{\boldsymbol{B}}_N}$ with $N~=~15$. From left to right column in each row: the SNRs equal $0~{\kern~3pt}{\rm~dB}$, $5~{\kern~3pt} ~~~~~~~~~{\rm~dB}$, and $\infty$, respectively. (Black dots: two centers detected. Red dots: one center detected.)

• Figure 3

Tomogram span as a function of range and elevation using a 21-by-21 window based on the real airborne dataset. Recovered results based on (a) actual six L-band 2D focused SAR complex image data using the conventional beamforing method, (b) actual six L-band 2D focused SAR complex image data using the wavelet-based CS method, and (c) the completed dataset of ten estimated optimal virtual baseline distribution using the wavelet-based CS method.

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Algorithm 1 Iterative algorithm for $L_1$ regularization reconstruction

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