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SCIENCE CHINA Information Sciences, Volume 60 , Issue 10 : 102305(2017) https://doi.org/10.1007/s11432-016-9017-6

Compressed sensing application in interferometric synthetic aperture radar

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  • ReceivedJul 9, 2016
  • AcceptedJan 21, 2017
  • PublishedJun 22, 2017

Abstract

A novel interferometric synthetic aperture radar (InSAR) signal processing method based on compressed sensing (CS) theory is investigated in this paper. InSAR image formation provides the scene reflectivity estimation along azimuth and range coordinates with the height information. While surveying the height information of the illuminated scene, the data volume enlarges. CS theory allows sparse sampling during the data acquisition, which can reduce the data volume and release the pressure on the record devices. InSAR system which configures two antennas to cancel the common backscatter random phase in each resolution element implies the sparse nature of the complex-valued InSAR image. The complex-valued image after conjugate multiplication that only a phase term proportional to the differential path delay is left becomes sparse in the transform domain. Sparse sampling such as M-sequence can be implemented during the data acquisition. CS theory can be introduced to the processing due to the sparsity and a link between raw data and interferometric complex-valued image can be built. By solving the CS inverse problem, the magnitude image and interferometric phase are generated at the same time. Results on both the simulated data and real data are presented. In comparison with the conventional SAR interferometry processing results, CS-based method shows the ability to keep the imaging quality with less data acquisition.


Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant No. 61271422).


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  • Figure 1

    (Color online) InSAR geometry projected on height-ground range plane.

  • Figure 2

    SAR image spectrum. (a) The spectrum before the backscatter random phase cancellation; (b) histogram of the original spectrum; (c) the spectrum after the backscatter random phase cancellation; (d) histogram of the spectrum after the backscatter random phase cancellation.

  • Figure 3

    InSAR data acquisition model.

  • Figure 6

    Simulated scene. (a) DEM; (b) ideal interferometric phase.

  • Figure 7

    RDA results (noise free). (a) Magnitude (all samples); (b) interferometric phase (all samples); (c) magnitude (50% samples); (d) interferometric phase (50% samples).

  • Figure 8

    CS results (noise free). (a) Magnitude (all samples); (b) interferometric phase (all samples); (c) magnitude (50% samples); (d) interferometric phase (50% samples).

  • Figure 9

    RDA results (SNR = $-$10 dB). (a) Magnitude (all samples); (b) interferometric phase (all samples); (c) magnitude (50% samples); (d) interferometric phase (50% samples).

  • Figure 10

    CS results (SNR = $-$10 dB). (a) Magnitude (all samples); (b) interferometric phase (all samples); (c) magnitude (50% samples); (d) interferometric phase (50% samples).

  • Figure 11

    Chirp scaling results. (a) Magnitude; (b) interferometric phase.

  • Figure 12

    Compressed sensing results (full samples). (a) Magnitude; (b) interferometric phase; (c) coherent coefficient.

  • Figure 13

    Compressed sensing results (50% samples). (a) Magnitude; (b) interferometric phase; (c) coherent coefficient.

  • Table 1   Simulation parameters
    Parameter Notation Value
    Carrier frequency $f_{\rm c}$ 35 GHz
    Incidence angle $\theta$ 35$^\circ$
    Baseline $B$ 1 m
    Platform height $H$ 3000 m
    Platform velocity $V_r$ 50 m/s
    Pulse repetition frequency PRF 200 Hz
    Range sampling rate $f_{\rm s}$ 600 MHz
    System bandwidth $B_{\rm s}$ 400 MHz
    Antenna size $D$ 0.6 m
  • Table 2   Simulation evaluation
    Window MSE MPE $\boldsymbol{\gamma_{\text{abs}}}$ $\boldsymbol{\gamma_{\text{phase}}}$
    Noise free
    RD$_1$ $5\times 5$ 0.4033 7.7318 0.9435 0.9885
    RD$_2$ $5\times 5$ 0.4246 16.1688 0.9405 0.8993
    CS$_1$ $5\times 5$ 0.3895 7.5999 0.9441 0.9834
    CS$_2$ $5\times 5$ 0.4117 11.8588 0.9428 0.9542
    RD$_1$ $7\times 7$ 0.3464 7.6803 0.9516 0.9878
    RD$_2$ $7\times 7$ 0.3795 13.6570 0.9495 0.9278
    CS$_1$ $7\times 7$ 0.3440 7.0813 0.9518 0.9875
    CS$_2$ $7\times 7$ 0.3714 9.6770 0.9503 0.9698
    SNR = 0
    RD$_1$ $5\times 5$ 0.4297 11.0752 0.9415 0.9839
    RD$_2$ $5\times 5$ 0.4639 20.0382 0.9387 0.8951
    CS$_1$ $5\times 5$ 0.4369 11.0750 0.9435 0.9831
    CS$_2$ $5\times 5$ 0.4455 15.4450 0.9409 0.9438
    RD$_1$ $7\times 7$ 0.4011 9.9295 0.9513 0.9871
    RD$_2$ $7\times 7$ 0.4258 16.2879 0.9498 0.9234
    CS$_1$ $7\times 7$ 0.4100 9.2649 0.9513 0.9842
    CS$_2$ $7\times 7$ 0.4155 12.7845 0.9503 0.9628
    SNR = $-$10 dB
    RD$_1$ $5\times 5$ 0.4449 23.1369 0.9359 0.9421
    RD$_2$ $5\times 5$ 0.4755 37.9985 0.9140 0.7699
    CS$_1$ $5\times 5$ 0.4350 23.1223 0.9358 0.9425
    CS$_2$ $5\times 5$ 0.4739 30.4115 0.9211 0.8413
    RD$_1$ $7\times 7$ 0.4235 19.3985 0.9422 0.9472
    RD$_2$ $7\times 7$ 0.4283 31.9880 0.9216 0.8096
    CS$_1$ $7\times 7$ 0.4149 19.2339 0.9422 0.9495
    CS$_2$ $7\times 7$ 0.4639 26.5798 0.9283 0.8667
  • Table 3   Real data results evaluation
    MSE MPE $\boldsymbol{\gamma_{\text{abs}}}$ $\boldsymbol{\gamma_{\text{phase}}}$
    CS$_1$ 0.0345 3.6981 0.9872 0.9501
    CS$_2$ 0.0392 9.2247 0.9534 0.9019

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