Compressive Sensing for Real-Time Microwave Imaging Systems Student : Hamed Kajbaf Faculty Advisor : Dr. Yahong Rosa Zheng Electrical and Computer Engineering Department Missouri University of Science and Technology, Rolla, MO 65409, USA Results Original DCT CS DFT CS 3D z = - 34 z = - 65 z = - 81 y (m m) x (m m) 0 30 60 90 120 0 30 60 90 120 150 180 y (m m) x (m m) 0 30 60 90 120 0 30 60 90 120 150 180 y (mm ) x (m m) 0 30 60 90 120 0 30 60 90 120 150 180 y (m m ) x (m m) 0 30 60 90 120 0 30 60 90 120 150 180 y (m m ) x (m m) 0 30 60 90 120 0 30 60 90 120 150 180 y (mm ) x (m m) 0 30 60 90 120 0 30 60 90 120 150 180 y (m m ) x (m m) 0 30 60 90 120 0 30 60 90 120 150 180 y (m m) x (m m) 0 30 60 90 120 0 30 60 90 120 150 180 y (m m ) x (m m) 0 30 60 90 120 0 30 60 90 120 150 180 0 10 20 30 40 50 60 70 80 90 100 0 0.05 0.1 0.15 0.2 D ata percentage N orm alized RM S erro DFT CS DCT CS 0 10 20 30 40 50 60 70 80 90 100 0 1 2 3 x 10 4 D ata percentage Iterations DFT CS DCT 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) 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 Hardware Setup z 0 Measurement Grid Sample Under Test x y -z a y a x 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 2D Fourier transform operator 2D inverse Fourier transform operator Inverse nonuniform Fourier transform operator Wavenumber Fourier transform variable corresponding to x Fourier transform variable SAR Image Reflection Coeff. Image Reconstruction c ΦΨ y c c ~ subject to ~ min 1 C ~ Ν , , y x f z y x s , , c ~ y Φ Ψ 0 2 2 2 4 2 1 1 2 , , , , z k k k j D NU D y x e y x f z y x s F F F 1 NU F D 2 F 1 2 D F x k k y k ,, f uv ,, sxyz