An efficient two-dimensional Chandrasekhar filter for restoration of images degraded by spatial blur and noise

In this paper, a new fast recursive filtering algorithm is proposed for the restoration of two-dimensional (2-D) images degraded by both spatial blur and additive white noise. It is assumed that the image is represented by a nonsymmetric half-plane (NSHP) model and the spatial blur is modeled by a finite extent spatially invariant, discrete, point spread function (PSF). A 2-D version of the Chandrasekhar filtering (CF) algorithm, which possesses better numerical properties and computational efficiency than the Kalman filtering (KF) algorithm, is developed. The computational requirements of the new algorithm are evaluated and compared to those of the 2-D KF algorithm. It is shown that for a 256 × 256 image, the 2-D CF algorithm requires less than 2.5 percent of the computational effort involved in the 2-D KF algorithm, and less than 12 percent of that involved in the 2-D reduced update Kalman filtering (RUKF) algorithm. Some experimental results based on a simulated image and a real image that demonstrate the filtering effectiveness and numerical stability of the new algorithm are also included.