DISPLACED PHASE CENTER ANTENNA SAR IMAGING

BASED ON COMPRESSED SENSING

Yueguan Lin 1,2,3, Bingchen Zhang 1,2, Wen Hong 1,2 and Yirong Wu 1,2

1 National Key Laboratory of Science and Technology on Microwave Imaging, P. R. China

2 Institute of Electronics, Chinese Academy of Sciences (IECAS), Beijing, P. R. China

3 Graduate University of Chinese Academy of Sciences (GUCAS), Beijing, P. R. China

Institute of Electronics, Chinese Academy of Sciences

National Key Laboratory of Microwave Imaging Technology

• Outlines

• Introduction

• DPCA SAR imaging based on Compressed Sensing

• Ground-based DPCA SAR experiment

• Conclusion and discussion

• Acknowledgement

• Introduction

• High azimuth resolution and wide unambiguous swath coverage are contradictive in SAR system design.

• DPCA SAR has the potential to achieve HRWS imaging. While there is a rigid restriction posed on its selection of PRF: SAR platform moves just one half of its total antenna length between subsequent radar pulses .

• When this condition is not satisfied, there will be nonuniform sampling in azimuth and rising azimuth ambiguities will appear under traditional imaging algorithms based on matched filter

• Introduction

• Krieger proposed A Doppler spectrum reconstruction algorithm *.

• This method can recover the unambiguous signal and suppress ambiguous energy.

• It is computation costly as inversions of matrix are involved and the reconstruction of spectrum should be carried out for every azimuth signal.

* Krieger, G., Gebert, N., and Moreira, A.: ‘Unambiguous SAR signal reconstruction from nonuniform displaced phase center sampling’. IEEE Geoscience and Remote Sensing Letters, 2004, 1(4): 260-264.

• DPCA SAR imaging based on Compressed Sensing

• Compressed Sensing X is sparse representable if there exists a sparsity basis that provides a K

sparse representation of it.

When Φ satisfies Restricted Isometry Property. The number of measurements needed to reconstruct the signal is not restrained by the Nyquist sampling rate, but by the complexity of the signal. We only need M measurements, where

where N is the number of measurements needed by the Nyquist Theorem

( )( )M O K N Klog /=

Y = ΦX

• DPCA SAR imaging based on Compressed Sensing

According to systems the DPCA SAR model can be constructed precisely

where ， y is the observations

x is observed scene

Φ is observation matrix

n is observation noise.

y Φx n

, 1,pk l P k P l Φ Φ

(1) 0 0 0 0

( 1) ( ) (1) 0 0

( ) ( 1) ( ) (1)

0 0 ( ) ( 1) (1)

0

0 0 0 0 ( )

p

p p p

p p p pp

p p p

p

h

h P h P h

h Q h Q h Q P h

h Q h P h

h Q

Φ

• DPCA SAR imaging based on Compressed Sensing

• The backscattering field of target is usually contributed by a few strong scattering centers, so CS is suitable in SAR imaging.

• As the observation is constructed precisely according to SAR system parameters, the ambiguity causes by nonuniform effective azimuth phase centers doesn’t exist.

• The observed scene can be reconstructed through solving an optimization problem

1 2min , subject to x y Φx

• Ground-based DPCA SAR experiment

Parameters Values

Carrier frequency 17 GHz

Based band width 1 GHz

Stepped frequencies 2.5 MHz

Span in azimuth [-1, 1] m

Azimuth sampling interval 0.024 m

Length of subaperture 0.032 m

Ground-based DPCA SAR system with one aperture transmitting stepped frequency and three apertures receiving echoes.

System parameters

DPCA SAR system

-0.03 -0.02 -0.01 0 0.01 0.02 0.03

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

Azimuth effective phase centers (m)

Azimuth effective phase centers

• Ground-based DPCA SAR experiment

Antennas Azimuth effective phase centers.

• Effective azimuth phase centers of this DPCA SAR system are nonuniformly

distributed.

-1 -0.5 0 0.5 1-50

-40

-30

-20

-10

0

Azimuth (m)

Ma

gn

itud

e (

dB

)

• Ground-based DPCA SAR experiment

Observed trihedral corner reflector. RD imaging without preprocessing

• Result using traditional Range-Doppler algorithm without preprocessing has -17dB ambiguities.

-1 -0.5 0 0.5 1-50

-40

-30

-20

-10

0

Azimuth (m)

Ma

gn

itud

e (

dB

)

-1 -0.5 0 0.5 1-50

-40

-30

-20

-10

0

Azimuth (m)

Ma

gn

itud

e (

dB

)

• Ground-based DPCA SAR experiment

RD imaging with spectrum reconstruction Proposed CS imaging

• Result using RD algorithm after spectrum reconstruction has -25dB ambiguities; result using proposed imaging algorithm with ambiguities being suppressed under -30dB.

• Conclusion and discussion

• DPCA SAR imaging algorithm based on CS can suppress the ambiguities caused by nonuniform sampling in azimuth and retrieve the target scene with high quality.

• The experimental results with ground-based DPCA SAR system validate its advantage.

We will evaluate this method’s performance with real space borne and airborne raw data in next step.

The effect of observation noise will be researched.

• Acknowledgement

• This work was supported by the State Key Development Program for Basic

Research of China (Grant No. 2010CB731905).

Thank you for your attention!Thank you for your attention!

Email: linyueguan@gmail.com