Compressive Sensing Operator Design and Optimization for Wideband 3-D Millimeter-Wave Imaging

This article proposes a design optimization method of fast compressive sensing (CS) operators for wideband three-dimensional (3-D) millimeter-wave (mmW) imaging systems. The proposed method consists of two parts: 1) a near-orthogonal 3-D mmW imaging operator design for avoiding large precomputed arrays and 2) a random antenna pattern design (compressive binary sampling matrix) for sparse sampling. The 3-D mmW imaging operator takes the nonlinear wavenumber relationship into account and uses a combination of truncation repair and sampling density compensation to eliminate the reconstruction error caused by truncating
$z$
and the nonuniform
$k_{z}$
sampling. The compressive binary sampling matrix minimizes grating lobes and suppresses residual grating lobes while maintaining the mainlobe width, by maximizing PeakSLL and maxPSF in the respective frequency range and 2-D measurement aperture. A
${Ka}$
-band (35–45 GHz) experiment utilizes the measurements of a very low sampling rate of 6.25% of fully sampled data to recover a high-resolution image. The result shows that the proposed CS operator reduces the maximum reconstruction error and the mean square error (MSE) between the recovered images from undersampled measurement and from the fully sampled data to
$10^{-15}$
and
$10^{-3}$
, respectively. Furthermore, the proposed decomposition method enables the soft thresholding in the CS iterative algorithms and simplifies the CS implementation in terms of antenna-array patterns, memory usage, and parallel computing. If the imaging system is implemented by a spatial antenna array, then the 6.25% sampling rate means that the number of antennas is reduced to 25% of the full-sampling system, thus reducing the cost. If the imaging system is implemented by raster scanning, then the CS implementation will reduce the number of spatial points to 25%, thus reducing the scan time. The number of frequency points is also reduced to 25%, which reduces the memory usage.