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SCIENCE CHINA Information Sciences
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SCIENCE CHINA Information Sciences, Volume 62 , Issue 4 : 049303(2019) https://doi.org/10.1007/s11432-018-9662-y

A novel iterative soft thresholding algorithm for $L_1$ regularization based SAR imageenhancement

Hui BI 1,2, Guoan BI 2,*
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  • ReceivedJul 27, 2018
  • AcceptedNov 15, 2018
  • PublishedFeb 26, 2019
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Abstract

There is no abstract available for this article.


Acknowledgment

This work was supported in part by Project of Temasek Laboratories@NTU and Scientific Research Starting Foundation of Nanjing University of Aeronautics and Astronautics (Grant No. 1004-YAH19009). We would like to thank Professor Jinpin SUN from Beihang University for providing the TerraSAR complex image data.


References

[1] Curlander J, Mcdonough R. Synthetic aperture radar: system and signal processing, New York: Wiley, 1991. Google Scholar

[2] Raney R K, Runge H, Bamler R. Precision SAR processing using chirp scaling. IEEE Trans Geosci Remote Sens, 1994, 32: 786-799 CrossRef ADS Google Scholar

[3] Cetin M, Karl W C. Feature-enhanced synthetic aperture radar image formation based on nonquadratic regularization. IEEE Trans Image Process, 2001, 10: 623-631 CrossRef PubMed ADS Google Scholar

[4] Patel V M, Easley G R, Healy D M. Compressed Synthetic Aperture Radar. IEEE J Sel Top Signal Process, 2010, 4: 244-254 CrossRef ADS Google Scholar

[5] Zhang B C, Hong W, Wu Y R. Sparse microwave imaging: Principles and applications. Sci China Inf Sci, 2012, 55: 1722-1754 CrossRef Google Scholar

[6] Bi H, Zhang B, Zhu X X. $L_{1}$ -Regularization-Based SAR Imaging and CFAR Detection via Complex Approximated Message Passing. IEEE Trans Geosci Remote Sens, 2017, 55: 3426-3440 CrossRef ADS Google Scholar

[7] Zhang B, Hong W, Bi H. L q regularisation-based synthetic aperture radar image feature enhancement via iterative thresholding algorithm. Electron Lett, 2016, 52: 1336-1338 CrossRef Google Scholar

[8] Bi H, Bi G, Zhang B. Complex-Image-Based Sparse SAR Imaging and its Equivalence. IEEE Trans Geosci Remote Sens, 2018, 56: 5006-5014 CrossRef ADS Google Scholar

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    Figure 1

    (Color online) Images reconstructed by different methods. (a) MF recovered image; (b) IST based algorithm recovered image; (c) sparse solution of the proposed BiIST based algorithm; (d) non-sparse solution of the proposed BiIST based algorithm. Phase difference between the MF based image and (e) IST based algorithm recovered result, (f) non-sparse solution of the proposed BiIST based algorithm, respectively.

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    Algorithm 1 BiIST for $L_1$ regularization basd SAR image feature enhancement

    Require:MF recovered complex image ${{{\boldsymbol~X}_{\rm~MF}}}$; Initial: $\displaystyle{{{\boldsymbol{X}}^{\left(~0~\right)}}~{\kern~3pt}=~{\kern~2pt}\boldsymbol{0}}$,

    ${\kern~33pt}\displaystyle{{{\boldsymbol{W}}^{\left(~0~\right)}}~=~{\kern~2pt}{\boldsymbol~X}_{\rm~MF}}$, ${\kern~33pt}$

    Error parameter $\varepsilon$, ${\kern~33pt}$Maximum iterative step ${{T}_{\max~}}$,

    while $0~\le~t~\le~{{T}_{\max~}}$ and ${\rm{Resi~>~}}\varepsilon$ do

    $\displaystyle{{{{\boldsymbol{\tilde~X}}}^{\left(~{t+1}~\right)}}~{\kern~3pt}=~~{\kern~7pt} {{\boldsymbol~W}^{\left(~t~\right)}}~{\kern~3pt}~+~{\kern~3pt}~{{\boldsymbol{X}}^{\left(~t~\right)}}}$,

    $\displaystyle{{\beta^{\left(t+1\right)}}~{\kern~6pt}~~=~{\kern~6pt}~{{{{| {{{\boldsymbol{\tilde~X}}^{(~t+1~)}}}|}_{K~+~1}}}~/~\mu~}}$,

    $\displaystyle{{{{\boldsymbol{W}}}^{\left(~{t+1}~\right)}}~{\kern~1pt}~=~~{\kern~7pt} {{\boldsymbol~X}_{\rm~MF}}~{\kern~3pt}~-~{\kern~3pt}~{{\boldsymbol{X}}^{\left(~t~\right)}}}$,

    $\displaystyle{{{{\boldsymbol{X}}}^{\left(~{t~+~1}~\right)}}{\kern~3pt}~=~{\kern~6pt} f~({{{{\boldsymbol{\tilde~X}}}^{\left(~{t~+~1}~\right)}};\mu{\beta^{\left~(t~+~1 \right~)}}}~)}$,

    $\displaystyle{{\rm{Resi}}{\kern~14pt}~=~{\kern~5pt}{\| {{{{\boldsymbol{X}}}^{\left(~{t~+~1}~\right)}}~-~{{{\boldsymbol{X}}}^{\left(~t~\right)}}}~\|_F}}$,

    $t~=~t+1$;

    end while

    Output:Recovered sparse image ${\boldsymbol{\hat~X}}~=~{{{\boldsymbol{X}}}^{\left(~{t}~\right)}}$. ${\kern~24pt}$Recovered non-sparse image ${\boldsymbol{\tilde~X}}~=~{{{\boldsymbol{\tilde~X}}}^{\left( {t}~\right)}}$.