Unsupervised 3-D restoration of tomographic images by constrained Wiener filtering

This communication presents a non-supervised restoration method based on a constrained Wiener filter. We implement our filter in the spatial domain and perform the filtering in 3-D. Our central contribution lies in the derivation of a cross validation based algorithm which estimates the noise variance from the observed image. Exploitation of the partitioned matrix inversion lemma leads to a reasonable computation time. Results indicate that the method is able to determine the noise variance with an accuracy sufficient to produce acceptable results in the restoration at low signal-to-noise ratios. However at higher signal-to-noise ratios (above 15 dB) some undersmoothing is observed.