We propose a method for feature-preserving regularized reconstruction in coherent imaging systems. In our framework, image formation from measured data is achieved through the minimization of a cost functional, designed to suppress noise artifacts while preserving features such as object boundaries in the reconstruction. The cost functional includes nonquadratic regularizing constraints. Our formulation effectively deals with the complex-valued and potentially random-phase nature of the scattered field, which is inherent in many coherent systems. We solve the challenging optimization problems posed in our framework by developing and using an extension of half-quadratic regularization methods. We present experimental results from three coherent imaging applications: digital holography, synthetic aperture radar, and ultrasound imaging. The proposed technique produces images where coherent speckle artifacts are effectively suppressed, and important features of the underlying scenes are preserved.