Compressive Sensing for Real-Time Microwave Imaging SystemsStudent: Hamed Kajbaf Faculty Advisor: Dr. Yahong Rosa Zheng

Electrical and Computer Engineering DepartmentMissouri University of Science and Technology, Rolla, MO 65409, USA

Results Performance and ComplexityOriginal DCT CS DFT CS

3D

z = - 34

z = - 65

z = - 81

y (mm)

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m)

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0 10 20 30 40 50 60 70 80 90 1000

0.05

0.1

0.15

0.2

Data percentage

Norm

aliz

ed R

MS

err

or

DFT CSDCT CS

0 10 20 30 40 50 60 70 80 90 1000

1

2

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x 104

Data percentage

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ns

DFT CSDCT CS

Conclusion Using CS for wideband SAR imaging saves 51%

of the acquisition time.

Application of CS to Wideband SAR Sparse representation in DFT and DCT domains

Recovering using basis pursuit (BP)

cΦΨycc

~subject to~min 1C~

Ν

Undersampled measurements Sampling matrix

Sparse representation Sparsifying matrix

Wideband Near-field SAR Imaging Application: Nondestructive Testing (NDT)

3D millimeter wave strip-map SAR imaging

Advantage: High resolution, depth penetration, nondestructive

Disadvantage: Slow raster scanning with traditional uniform grid full measurement

Hardware Setup

z0

Measurement Grid

Sample Under Test

x

y

-z

ay

ax

,, yxf

zyxs ,,

c~

yΦ

Ψ

Experimental Tests 9 round rubber pads: 5 mm diameter

Swept frequency in 35.04 to 44.96 GHz (Q-band)

Steps of 2mm along X and Y direction

Complete data: 2947 sec

Undersampled: 35% of spatial points: 1450 sec

Future Work Use the 3D SAR as the sparse representation to

improve the quality of the recovered images.

Make the selection of sparse representation adaptive.

Acknowledgements This work was supported in part by the Intelligent

System Center, ASNT fellowship, and by University of Missouri Research Board fund.

Objective Acquire reflection coefficients at random

position and frequencies to reduce the acquisition time.

Recover the SAR images applying compressed sensing (CS) using 35% of spatial and 20% of frequency samples

0

2224

211

2 ,,,,zkkkj

DNUDyxeyxfzyxs FFF

2D Fourier transform operator

2D inverse Fourier transform operator

Inverse nonuniform Fourier transform operator

Wavenumber

Fourier transform variable corresponding to x

Fourier transform variable corresponding to y

1NUF

D2F1

2DF

xkk

yk

, ,f u v

, ,s x y z

SAR Image

Reflection Coeff.

Image Reconstruction