The filters where and are shown in Fig (6.10) for M=1. We note from Fig (6.10) that decreases relative to , more noise smoothing is performed. Referring back to fig (6.9), to measure the local signal detail in the system, the algorithm developed uses the signal variance .

The specific method used to design the space-variant is given by (6.3.3) .

This filter is typically a small FIR filter of size say or or . Hence pixel by pixel processing is employed. Since may be estimated from by,

	if     is

where

The local mean estimate can be obtained from (6.3.2) and is assumed known.

In the method described above, unlike non-adaptive Wiener filter, the processed image has a significant amount of noise reduction without noticeable blurring.

Figure 6.10 Impulse response of a space-variant image restoration filter as a function of and

Short-Space Spectral Subtraction:

This method to reduce additive noise is a straight forward extension of method developed to reduce additive random noise in speech.

We consider subimage by subimage processing by applying a window to the degraded image i.e.

The window is chosen s.t. the subimage can be assumed approximately stationary.

with and - denoting Fourier Transforms, we obtain,

or,		(6.3.4)

In this method is estimated based on equation (6.3.4)

From the degraded subimage can be obtained directly.

The terms and can not be obtained exactly and are approximated by and .