A Hyperparameter-free Total Variation Regularization Method for Real Aperture Radar Angular Super-resolution

A real aperture radar has physical space limitations that result in a wide antenna beam, leading to low angular resolution. The angular super-resolution method based on sparse reconstruction introduces sparse prior constraints of the target under a regularization framework and reconstructs the target reflectivity function through iterative optimization, thereby significantly enhancing the angular resolution of the radar. However, existing sparse reconstruction methods primarily consider the sparse distribution characteristics of strong point targets, neglecting the contour information of extended targets, which results in distortion in the recovery of target edges. Additionally, these methods are sensitive to one or more hyperparameters introduced into the cost function. Thus, meticulous manual adjustments are essential in practical applications, and they pose challenges in terms of the adaptive selection of hyperparameters in dynamic scenarios. To address these issues, this paper proposes a hyperparameter-free Total Variation (TV) regularization angular super-resolution method. First, a square-root Least Absolute Shrinkage and Selection Operator (LASSO) cost function was established to characterize the fitting residuals between the scan echo sequence and target reflectivity function and to characterize the sparse constraints on the target edge gradients. Using this function, the target contour reconstruction problem was transformed into a non-smooth convex optimization problem under TV regularization constraints. The analytical expression of the hyperparameter-free TV regularization term was derived based on the covariance fitting criterion. Finally, a Generalized Iteratively Reweighted Least Squares (GIRLS) strategy was proposed, and an iterative optimization method for solving the non-smooth convex optimization problem of square-root LASSO was derived. The simulation and experimental results demonstrate that the proposed method improves angular resolution of the radar while preserving the contour information of the target without requiring manual adjustment of the hyperparameters.