We propose a method for edge-preserving regularized reconstruction in coherent imaging systems. In our framework, image formation from measured data is achieved through the minimization of a cost function, which includes nonquadratic regularizing constraints for suppressing noise artifacts, while preserving the object boundaries in the reconstruction. The cost function we use effectively deals with the complex-valued and 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 a novel extension of half-quadratic regularization methods. We present experimental results from three coherent imaging applications: digital holography, synthetic aperture radar, and medical ultrasound. The proposed technique produces images where coherent speckle artifacts are effectively suppressed, and boundaries between different regions in the scene are preserved.
Alan S. Willsky, Müjdat Çetin, William