On the performance of compressed sensing-based methods for millimeter-wave holographic imaging

This paper investigates compressed sensing (CS) based methods for reducing data-acquisition time in 2D millimeter-wave holographic imaging systems. Specific attention is paid to situations where the array element spacing does not satisfy the Nyquist criterion due to physical limitations. Simulation and experimental results demonstrate that CS methods achieve better reconstruction than the conventional backpropagation method with undersampled data at the cost of increased computational complexity. Specifically, the definition-based CS (D-CS) method derived by discretizing the scattering model achieves the best image resolution but can produce ghost targets when the sampling interval is greater than approximately twice the Nyquist sampling interval. On the contrary, the Fourier-transform-based CS (FT-CS) method has relatively lower resolution but performs well in the case of low number of measurements, large sampling interval, and low transmit power. In addition, the D-CS method requires much higher time complexity and space complexity than the FT-CS method because the 2D data needs to be processed in vector form. Particularly, the space complexity of constructing and loading the dictionary matrix makes the D-CS method extremely inefficient in dealing with real-time applications. The overall algorithm running time of the D-CS method can be up to 50 times greater than the FT-CS method with a scanning aperture of 81×81 and 121×121 grid size in reconstruction. An efficient method is to use the FT-CS method for coarse imaging and then use the D-CS method for specific regions where better precision is required.