Fast sparse image reconstruction method in through-the-wall radars using limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm

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.

Automated summary

Compressed sensing has revolutionized through-the-wall radar imaging by allowing image signal recovery using a portion of data, however, nonlinear methods have increased computational costs, limiting practical applications. This study introduces the use of LBFGS algorithm to lower image reconstruction time, achieving an 87% reduction in computational time relative to classical methods, even under scenarios with increased targets or data volume. The proposed method remains robust in noisy environments, demonstrating its potential in practical applications.