TAILIEUCHUNG - The Essential Guide to Image Processing- P12

The Essential Guide to Image Processing- P12:We are in the middle of an exciting period of time in the field of image processing. Indeed, scarcely a week passes where we do not hear an announcement of some new technological breakthrough in the areas of digital computation and telecommunication. | Image Restoration Algorithms 335 TABLE Prediction coefficients and variance of v n1 n2 for four images computed in the MSE optimal sense by the Yule-Walker equations. 0 1 41 1 1 0 v Cameraman Lena Trevor White White noise shortcomings. More elaborate estimators for the power spectrum exist but these require much more a priori knowledge. Asecond approach is to estimate the power spectrum Sf u v from a set of representative images. These representative images are to be taken from a collection of images that have a content similar to the image that needs to be restored. Of course one still needs an appropriate estimator to obtain the power spectrum from the set of representative images. The third and final approach is to use a statistical model for the ideal image. Often these models incorporate parameters that can be tuned to the actual image being used. A widely used image model not only popular in image restoration but also in image compression is the following 2D causal autoregressive model 9 f ni n2 a0 if ni n2 - 1 ai if ni - 1 n2 - 1 ai of ni - 1 n2 v ni n2 . In this model the intensities at the spatial location n1 n2 are described as the sum of weighted intensities at neighboring spatial locations and a small unpredictable component v n1 n2 . The unpredictable component is often modeled as white noise with variance av. Table gives numerical examples for MSE estimates of the prediction coefficients aij for some images. For the MSE estimation of these parameters the 2D autocorrelation function has first been estimated and then used in the Yule-Walker equations 9 . Once the model parameters for have been chosen the power spectrum can be calculated to be equal to Sf u v ---------------------------------2 . i - ao ie-ju - ai ie-ju-jv - a e j 2 The tradeoff between noise smoothing and deblurring that is made by the Wiener filter is

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