Compressive sensing for microwave and millimeter-wave array imaging

Compressive Sensing (CS) is a recently proposed signal processing technique that has already found many applications in microwave and millimeter-wave imaging. CS theory guarantees that sparse or compressible signals can be recovered from far fewer measure- ments than those were traditionally thought necessary. This property coincides with the goal of personnel surveillance imaging whose priority is to reduce the scanning time as much as possible. Therefore, this thesis investigates the implementation of CS techniques in personnel surveillance imaging systems with different array configurations. The first key contribution is the comparative study of CS methods in a switched array imaging system. Specific attention has been paid to situations where the array element spacing does not satisfy the Nyquist criterion due to physical limitations. CS methods are divided into the Fourier transform based CS (FT-CS) method that relies on conventional FT and the direct CS (D-CS) method that directly utilizes classic CS formulations. The performance of the two CS methods is compared with the conventional FT method in terms of resolution, computational complexity, robustness to noise and under-sampling. Particularly, the resolving power of the two CS methods is studied under various cir- cumstances. Both numerical and experimental results demonstrate the superiority of CS methods. The FT-CS and D-CS methods are complementary techniques that can be used together for optimized efficiency and image reconstruction. The second contribution is a novel 3-D compressive phased array imaging algorithm based on a more general forward model that takes antenna factors into consideration. Imaging results in both range and cross-range dimensions show better performance than the conventional FT method. Furthermore, suggestions on how to design the sensing con- figurations for better CS reconstruction results are provided based on coherence analysis. This work further considers the near-field imaging with a near-field focusing technique integrated into the CS framework. Simulation results show better robustness against noise and interfering targets from the background. The third contribution presents the effects of array configurations on the performance of the D-CS method. Compressive MIMO array imaging is first derived and demonstrated with a cross-shaped MIMO array. The switched array, MIMO array and phased array are then investigated together under the compressive imaging framework. All three methods have similar resolution due to the same effective aperture. As an alternative scheme for the switched array, the MIMO array is able to achieve comparable performance with far fewer antenna elements. While all three array configurations are capable of imaging with sub-Nyquist element spacing, the phased array is more sensitive to this element spacing factor. Nevertheless, the phased array configuration achieves the best robustness against noise at the cost of higher computational complexity. The final contribution is the design of a novel low-cost beam-steering imaging system using a flat Luneburg lens. The idea is to use a switched array at the focal plane of the Luneburg lens to control the beam-steering. By sequentially exciting each element, the lens forms directive beams to scan the region of interest. The adoption of CS for image reconstruction enables high resolution and also data under-sampling. Numerical simulations based on mechanically scanned data are conducted to verify the proposed imaging system.