The inverse filtering approach has poor performance. The wiener filtering approach uses the degradation function and statistical characteristics of noise into the restoration process.The objective is to find an estimate of the uncorrupted image f such that the mean square error between them is minimized.
The error measure is given by
Where E{.} is the expected value of the argument.
We assume that the noise and the image are uncorrelated one or the other has zero mean. The gray levels in the estimate are a linear function of the levels in the degraded image
Here, H(u,v)= degradation function,
H(u,v)=complex conjugate of H(u,v) | H(u,v)|2=H (u,v) H(u,v)
Sn(u,v)=|N(u,v)|2= power spectrum of the noise
Sf(u,v)=|F(u,v)|2= power spectrum of the underrated image
The power spectrum of the undegraded image is rarely known. An approach used frequently when these quantities are not known or cannot be estimated then the expression used is
Where K is a specified constant.