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.