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SCIENCE CHINA Information Sciences, Volume 60, Issue 10: 109302(2017) https://doi.org/10.1007/s11432-016-0529-6

An efficient data compression technique based on BPDN for scattered fields from complex targets

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  • ReceivedAug 25, 2016
  • AcceptedNov 9, 2016
  • PublishedFeb 20, 2017

Abstract

There is no abstract available for this article.


Acknowledgment

This work was supported by the CAS/SAFEA International Partnership Program for Creative Research Team (Grant No. Y313110240).


Supplement

Tables A1, A2, Figure A1.


References

[1] Keller J B. Geometrical Theory of Diffraction*. J Opt Soc Am, 1962, 52: 116-130 CrossRef Google Scholar

[2] Chang L C T, Gupta I J, Burnside W D. A data compression technique for scattered fields from complex targets. IEEE Trans Antennas Propagat, 1997, 45: 1245-1251 CrossRef ADS Google Scholar

[3] Bhalla R, Ling H. Three-dimensional scattering center extraction using the shooting and bouncing ray technique. IEEE Trans Antennas Propag, 1996, 44: 1445--1453. Google Scholar

[4] Chen S S, Donoho D L, Saunders M A. Atomic decomposition by basis pursuit. SIAM Rev, 2001, 43: 129--159. Google Scholar

[5] Berg E van den, Friedlander M P. Probing the Pareto frontier for basis pursuit solutions. SIAM J Sci Comput, 2008, 31: 890--912. Google Scholar

[6] Desai M D, Jenkins W K. Convolution backprojection image reconstruction for spotlight mode synthetic aperture radar. IEEE Trans Image Process, 1992, 1: 505--517. Google Scholar

[7] Quan X Y, Zhang B C, Liu J G, et al. An efficient general algorithm for SAR imaging: complex approximate message passing combined with backprojection. IEEE Geosci Remote Sens Lett, 2016, 13: 535--539. Google Scholar

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    Algorithm 1 RCS data compression based on BPDN

    Require:RCS samples $\boldsymbol{y}$, additive noise level $\sigma \in \left[ {0,{{\left\| {\boldsymbol{y}} \right\|}_2}} \right)$, optimality tolerance ${T_{\text{op}}} \geqslant 0$, sufficient descent parameter $\eta \in \left( {0,1} \right)$, maximum and minimum step lengths ${\alpha _{\max }} > {\alpha _{\min }} > 0$, output threshold ${T_{\text{v}}} < 0\,{\text{dB}}$;

    Output:valid backscattering coefficients ${\boldsymbol{\hat x}}$;

    Output:${{\boldsymbol{x}}^0} = \bf{0}$, ${{\boldsymbol{r}}^0} = {\boldsymbol{y}}$, ${\tau ^0} = 0$, ${\alpha ^0} = {\alpha _{\max }}$;

    for $p = 1$ to ${\text{maxite}}{{\text{r}}_1}$

    if ${{\left| {{{\left\| {{{\boldsymbol{r}}^{p - 1}}} \right\|}_2} - \sigma } \right|} \mathord{\left/ {\vphantom {{\left| {{{\left\| {{{\boldsymbol{r}}^{p - 1}}} \right\|}_2} - \sigma } \right|} {{{\left\| {{{\boldsymbol{r}}^{p - 1}}} \right\|}_2}}}} \right. \kern-\nulldelimiterspace} {{{\left\| {{{\boldsymbol{r}}^{p - 1}}} \right\|}_2}}} \leqslant {T_{{\text{op}}}}$ then

    break;

    end if

    ${\tau ^p} = {\tau ^{p - 1}} - \left( {\sigma - {{\left\| {{\boldsymbol{r}}^{p - 1}} \right\|}_2}} \right)\tfrac{{\left\| {{\boldsymbol{r}}^{p - 1}} \right\|}_2}{{\left\| {{\mathcal{I}}\left( {{\boldsymbol{r}}^{p - 1}} \right)} \right\|}_\infty }$;

    if ${\tau ^p} < {\tau ^{p - 1}}$ then

    ${{\boldsymbol{\tilde x}}^0} = {{\mathcal{P}}_{{\tau ^p}}}\left( {{{\boldsymbol{x}}^{p - 1}}} \right)$, ${{\boldsymbol{\tilde r}}^0} = {\boldsymbol{y}} - {\mathcal{G}}\left( {{{{\boldsymbol{\tilde x}}}^0}} \right)$, ${{\boldsymbol{\tilde g}}^0} = - {\mathcal{I}}\left( {{{{\boldsymbol{\tilde r}}}^0}} \right)$;

    else

    ${{\boldsymbol{\tilde x}}^0} = {{\boldsymbol{x}}^{p - 1}}$, ${{\boldsymbol{\tilde r}}^0} = {{\boldsymbol{r}}^{p - 1}}$, ${{\boldsymbol{\tilde g}}^0} = - {\mathcal{I}}\left( {{{{\boldsymbol{\tilde r}}}^0}} \right)$;

    end if

    for $q = 1$ to ${\text{maxite}}{{\text{r}}_2}$

    if ${\delta _{{\tau ^p}}}\left( {{{{\boldsymbol{\tilde r}}}^{q - 1}}} \right) \leqslant {T_{{\text{op}}}}$ then

    break;

    end if

    $\alpha = {\alpha ^{q - 1}}$;

    for $h = 1$ to ${\text{maxite}}{{\text{r}}_3}$

    ${\boldsymbol{\bar x}} = {{\mathcal{P}}_{{\tau ^p}}}\left( {{{{\boldsymbol{\tilde x}}}^{q - 1}} - \alpha {{{\boldsymbol{\tilde g}}}^{q - 1}}} \right)$, ${\boldsymbol{\bar r}} = {\boldsymbol{y}} - {\mathcal{G}}\left( {{\boldsymbol{\bar x}}} \right)$;

    if $\left\| {{\boldsymbol{\bar r}}} \right\|_2^2 \leqslant \left\| {{{{\boldsymbol{\tilde r}}}^{q - 1}}} \right\|_2^2 + \eta {\left( {{\boldsymbol{\bar x}} - {{{\boldsymbol{\tilde x}}}^{q - 1}}} \right)^H}{{\boldsymbol{\tilde g}}^{q - 1}}$ then

    break;

    else

    $\alpha = {\alpha \mathord{\left/ {\vphantom {\alpha 2}} \right. \kern-\nulldelimiterspace} 2}$;

    end if

    $h = h + 1$;

    end for

    ${{\boldsymbol{\tilde x}}^q} = {\boldsymbol{\bar x}}$, ${{\boldsymbol{\tilde r}}^q} = {\boldsymbol{\bar r}}$, ${{\boldsymbol{\tilde g}}^q} = - {\mathcal{I}}\left( {{{{\boldsymbol{\tilde r}}}^q}} \right)$, $\Delta {\boldsymbol{x}} = {{\boldsymbol{\tilde x}}^q} - {{\boldsymbol{\tilde x}}^{q - 1}}$, $\Delta {\boldsymbol{g}} = {{\boldsymbol{\tilde g}}^q} - {{\boldsymbol{\tilde g}}^{q - 1}}$;

    if $\Delta {{\boldsymbol{x}}^{\rm H}}\Delta {\boldsymbol{g}} \leqslant 0$ then

    ${\alpha ^q} = {\alpha _{\max }}$;

    else

    ${\alpha ^q} = \min \left( {{\alpha _{\max }},\max \left( {{\alpha _{\min }},\tfrac{{\left\| {\Delta {\boldsymbol{x}}} \right\|_2^2}}{{\Delta {{\boldsymbol{x}}^H}\Delta {\boldsymbol{g}}}}} \right)} \right)$;

    end if

    $q = q + 1$;

    end for

    ${{\boldsymbol{x}}^p} = {{\boldsymbol{\tilde x}}^{q - 1}}$, ${{\boldsymbol{r}}^p} = {{\boldsymbol{\tilde r}}^{q - 1}}$, $p = p + 1$;

    end for

    return ${\boldsymbol{\hat x}}\! =\! \left\{ {x_n^{p - 1} \in {{\boldsymbol{x}}^{p - 1}}\left| {20\lg \left( {\tfrac{{\left| {x_n^{p - 1}} \right|}}{\max \left( {\left| {{\boldsymbol{x}}^{p - 1}}\! \right|}\! \right)}}\! \right)\! \geqslant \! {T_{\text{v}}}} \right.} \right\}$;

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