Wiener Filter technique is widely used in inverse problem (deconvolution), especially for image restoration. However, there exist many deconvolution schemes, such as Wiener Filter with auto-regressive models, regularized solutions, spectral extrapolation, minimum variance deconvolution, curve fitting methods, homomorphic deconvolutions (through Cepstrum), or even the simple least mean squares. Can anyone tell me about the advantages of Wiener Filter compared with other deconvolution techniques?
I think it is very easy to be used in waveform or image inverse, and you can easily coding. But the difficult in the signal processing is how to detemine the parameters.
Wiener filter is the solution to Tikhonov's cost function when your operator is a circular matrix, which corresponds to the circular convolution/deconvolution operation. The performance of Tikhonov regularization depends on the operator and measurements used. In other words, the performance of the Wiener filter can be very good in some cases, and less good in others..
As Guoming wrote, it has a good compromise between computational efficiency and quality of the reconstruction. Its main advantage is that it can be efficiently calculated with the FFT and the solution is in a closed form. For finding the regularisation parameter, the L-curve or Generalized cross-validation methods are usually used. P. C. Hansen's book on inverse problems is a good introduction to this topic.
If your deconvolved signals have sparsity, you could also look into the LASSO method.
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