Imaging Method of Downward-Looking 3D Synthetic Aperture Radar Based on Multiple Measurement Vectors Model

Le Kang; Qun Zhang; Yichang Chen; Qiyong Liu

doi:10.3788/AOS201737.1111003

Journals >Acta Optica Sinica >Volume 37 >Issue 11 >Page 1111003 > Article

Acta Optica Sinica
Vol. 37, Issue 11, 1111003 (2017)

Imaging Method of Downward-Looking 3D Synthetic Aperture Radar Based on Multiple Measurement Vectors Model

Le Kang^1、2、*, Qun Zhang^1、2、3, Yichang Chen^1、2, and Qiyong Liu^1、2

Author Affiliations

¹ College of Information and Navigation, Air Force Engineering University, Xi'an, Shaanxi 710077, China

² Collaborative Innovation Center of Information Sensing and Understanding, Xi'an, Shaanxi 710077, China

³ Key Laboratory for Information Science of Electromagnetic Waves, Fudan University, Shanghai 200433, China

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DOI: 10.3788/AOS201737.1111003 Cite this Article Set citation alerts

Le Kang, Qun Zhang, Yichang Chen, Qiyong Liu. Imaging Method of Downward-Looking 3D Synthetic Aperture Radar Based on Multiple Measurement Vectors Model[J]. Acta Optica Sinica, 2017, 37(11): 1111003 Copy Citation Text

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Fig. 1. Imaging mode of DL 3D SAR

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Fig. 2. Workflow of the SMV-based DL 3D SAR imaging

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Fig. 3. Workflow of the MMV-based DL 3D SAR imaging

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Fig. 4. Relationship curves of the sampling number and reconstruction accuracy. (a) 5 scattering points; (b) 10 scattering points

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Fig. 5. Relationship curves of observation multiplicity, signal-to-noise ratio and reconstruction accuracy

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Fig. 6. 3D imaging scene

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Fig. 7. 3D imaging results of different methods. (a) MMV-based method; (b) SMV-based method; (c) proposed method

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Fig. 8. Along-cross-track planes of different methods. (a) MMV-based method; (b) SMV-based method; (c) proposed method

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Inputs: measurement vector y, sensing matrix A, sparse level K;

Initializations: residue error vector r=y, support set Ω=∅; for k=1:K; step 1: Obtain support, η_k←argmax

\begin{matrix} |A^{H} *r| \end{matrix}

; step 2: Update support set Ω=Ω∪{η_k}; step 3: Solution of least square ρ=

\begin{matrix} (A {(:, Ω)}^{H} A {(:, Ω))}^{- 1} \end{matrix}

A(:,Ω)^H*y; step 4: Update residual r=y-A(:,Ω)*ρ; end step 5:

\begin{matrix} \hat{x} \end{matrix}

(Ω)=ρ;outputs: The sparse signal

\begin{matrix} \hat{x} \end{matrix}

, residue error vector r.

Table 1. OMP algorithm

Inputs: measurement matrix Y, sensing matrix A, sparse level K;

Initializations: X=0, residue error Matrix R=Y, support set Ω=∅; for k=1:K; step 1: Obtain support, η_k←argmax

\begin{matrix} ‖ A^{H} * R^{(i)} ‖_{1,1} \end{matrix}

; step 2: Update support set Ω=Ω∪{η_k}; step 3: Solution of least square

\begin{matrix} \hat{X} \end{matrix}

(Ω,:)=

\begin{matrix} (A {(:, Ω)}^{H} A {(:, Ω))}^{- 1} \end{matrix}

A(:,Ω)^H*R⁽ⁱ⁾; step 4: Update residual R⁽ⁱ⁾=Y⁽ⁱ⁾-A(:,Ω)*

\begin{matrix} \hat{X} \end{matrix}

(Ω,:); endoutputs: The sparse signal

\begin{matrix} \hat{X} \end{matrix}

, residue error matrix R.

Table 2. Extended OMP algorithm

Operation	SMV-based method	MMV-based method
Obtain the support	O(2KN_rM)	O(2KN_rM)
Solution of least square	O(2KN_rM)	O(2KN_rM/L)

Table 3. Analysis of complexity

Parameter	Value	Parameter	Value
Carrier frequency /GHz	37.5	Radar velocity /(m·s^-1)	50
Pulse bandwidth /MHz	300	Number of antenna elements	128
Chirp duration /μs	1.0	Along-track resolution /m	0.4
Radar height /m	500	Range resolution /m	0.5
Cross-track resolution /m	0.4

Table 4. Simulation parameter

Performance	SMV based imaging method		MMV-based method
Performance	L=1		L=4	L=16	L=64	L=128
Mean running time /s	207.60		122.30	65.52	47.19	33.17

Table 5. Running time of methods

Le Kang, Qun Zhang, Yichang Chen, Qiyong Liu. Imaging Method of Downward-Looking 3D Synthetic Aperture Radar Based on Multiple Measurement Vectors Model[J]. Acta Optica Sinica, 2017, 37(11): 1111003

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