The feature-enhanced regularization-based radar image formation technique can effectively obtain high resolution image with speckle and sidelobe artifacts suppressed. Hype-parameter selection is vital for the quality of the regularizing image. The Generalized Cross Validation(GCV), Robust Generalized Cross Validation(RGCV) and Stein’s Unbias Risk Estimator(SURE) methods are applied in the non-quadratic regularization and the close form expressions of GCV, RGCV and SURE function are deduced. A fast algorithm and a generalized fix-point iteration algorithm are proposed to solve the regularization problem when the regularizing item is amended. The algorithm can be used for adaptive selection of the hyper-parameter. Numeric simulation proves the effectiveness of the proposed method.