An iterative method for restoring noisy images

A new iterative image restoration method is presented which incorporates a priori knowledge concerning the image and noise statistics directly in the iterative procedure. The iterative algorithm is computationally efficient in that only a small number of computations per pixel are required and appears to exhibit neither high noise sensitivity nor significant loss of resolution. It is demonstrated that for image signal-to-noise ratio,
L
, greater than some
L_{\min}
, the procedure converges to the best mean-square estimate of the image. The value of
L_{\min}
is derived and shown to depend on the correlation parameters of the image model. The basic iterative algorithm is then modified so that the modified algorithm converges to the best mean-square estimate of the image for all values of L. An interesting feature of this technique is that the noisy observed image is taken as the initial approximation to the best estimate. In general, an attractive advantage of iterative algorithms for image restoration is that they readily facilitate man-machine interaction.