Restoration of stochastically blurred images by the geometrical mean filter

The restoration of images degraded by a stochastic point spread function and additive detection noise is examined. Previously, the optimization criterion of the Wiener technique was applied successfully to this problem. However, when the strengths ofthe noise sources are not small, the restoration results of this method become noisy, albeit the deblurring results are of good quality. First, to obtain smoother restoration, the constrained least squares deconvolution method was developed. The objective function chosen was the one which yields smooth restoration. The restoration results of this filter were very smooth, as expected, but the deblurring was not as effective as that of the Wiener technique. Then, a geometrical mean filter that combines both the Wiener and the constrained least squares criteria was developed. This resulted in restored pictures that were both smooth and deblurred. The two filters developed are computationally inexpensive since they both can be implemented in the Fourier domain using the circulant matrix approximation.