Compressive Sensing Operator Design and Optimization for Wideband 3-D Millimeter-Wave Imaging
Compressive Sensing Operator Design and Optimization for Wideband 3-D Millimeter-Wave Imaging
复制标题
宽带三维毫米波成像压缩传感算子的设计与优化
DOI：
10.1109/tmtt.2021.3100499
复制
发表时间：
2022-01
影响因子：
4.3
通讯作者：
Dongjie Bi;Xifeng Li;Xuan Xie;Yongle Xie;Y. R. Zheng
中科院分区：
文献类型：
--
作者：
Dongjie Bi;Xifeng Li;Xuan Xie;Yongle Xie;Y. R. Zheng
本文提出了一种用于宽带三维（3-D）毫米波（mmW）成像系统的快速压缩感知（CS）算子的设计优化方法。所提出的方法由两部分组成：1）用于避免大型预计算阵列的近正交 3-D mmW 成像算子设计；2）用于稀疏采样的随机天线方向图设计（压缩二进制采样矩阵）。 3-D mmW成像算子考虑非线性波数关系，采用截断修复和采样密度补偿相结合的方法，消除截断$z$和非均匀$k_{z}$采样带来的重建误差。压缩二进制采样矩阵通过在各自的频率范围和二维测量孔径中最大化 PeakSLL 和 maxPSF，最大限度地减少栅瓣并抑制残余栅瓣，同时保持主瓣宽度。 ${Ka}$ 频段 (35–45 GHz) 实验利用完全采样数据的 6.25% 极低采样率的测量来恢复高分辨率图像。结果表明，所提出的 CS 算子将欠采样测量恢复图像和完全采样数据恢复图像之间的最大重建误差和均方误差 (MSE) 分别降低到 $10^{-15}$ 和 $10^{-3}$ 。此外，所提出的分解方法支持 CS 迭代算法中的软阈值处理，并在天线阵列模式、内存使用和并行计算方面简化了 CS 实现。如果成像系统采用空间天线阵列实现，那么6.25%的采样率意味着天线数量减少到全采样系统的25%，从而降低了成本。如果成像系统是通过光栅扫描实现的，那么CS实现会将空间点的数量减少到25%，从而减少扫描时间。频点数量也减少到25%，从而减少了内存占用。
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.