Compressed sensing allows recovery of image signals using a portion of data – a technique that has drastically revolutionized the field of through-the-wall radar imaging (TWRI). This technique can be accomplished through nonlinear methods, including convex programming and greedy iterative algorithms. However, such (nonlinear) methods increase the computational cost at the sensing and reconstruction stages, thus limiting the application of TWRI in delicate practical tasks (e.g. military operations and rescue missions) that demand fast response times. Motivated by this limitation, the current work introduces the use of a numerical optimization algorithm, called Limited Memory Broyden–Fletcher–Goldfarb–Shanno (LBFGS), to the TWRI framework to lower image reconstruction time. LBFGS, a well-known Quasi-Newton algorithm, has traditionally been applied to solve large scale optimization problems. Despite its potential applications, this algorithm has not been extensively applied in TWRI. Therefore, guided by LBFGS and using the Euclidean norm, we employed the regularized least square method to solve the cost function of the TWRI problem. Simulation results show that our method reduces the computational time by 87% relative to the classical method, even under situations of increased number of targets or large data volume. Moreover, the results show that the proposed method remains robust when applied to noisy environment.

压缩传感允许使用部分数据恢复图像信号——这项技术彻底改变了穿墙雷达成像 (TWRI) 领域。这种技术可以通过非线性方法来实现，包括凸规划和贪心迭代算法。然而，这种（非线性）方法增加了传感和重建阶段的计算成本，从而限制了 TWRI 在需要快速响应时间的精细实际任务（例如军事行动和救援任务）中的应用。受此限制的启发，目前的工作在 TWRI 框架中引入了一种名为 Limited Memory Broyden–Fletcher–Goldfarb–Shanno (LBFGS) 的数值优化算法，以降低图像重建时间。LBFGS，一种著名的拟牛顿算法，传统上用于解决大规模优化问题。尽管有潜在的应用，但该算法尚未在 TWRI 中广泛应用。因此，以LBFGS为指导，使用欧几里得范数，我们采用正则化最小二乘法求解TWRI问题的代价函数。仿真结果表明，即使在目标数量增加或数据量较大的情况下，我们的方法相对于经典方法减少了 87% 的计算时间。此外，结果表明，该方法在应用于嘈杂环境时仍然具有鲁棒性。我们采用正则化最小二乘法来解决 TWRI 问题的成本函数。仿真结果表明，即使在目标数量增加或数据量较大的情况下，我们的方法相对于经典方法减少了 87% 的计算时间。此外，结果表明，该方法在应用于嘈杂环境时仍然具有鲁棒性。我们采用正则化最小二乘法来解决 TWRI 问题的成本函数。仿真结果表明，即使在目标数量增加或数据量较大的情况下，我们的方法相对于经典方法减少了 87% 的计算时间。此外，结果表明，该方法在应用于嘈杂环境时仍然具有鲁棒性。