Die Hilberttransformation und ihre Verallgemeinerung in Optik und Bildverarbeitung

Two applications accentuate the importance of the referred transform. At once this well known example of a singular integral transform appears naturally in the Schlieren method, where all the spectra on one side of the central order are excluded to obtain information about phase objects. The other application is the computerized tomography. There we get the reconstructed images about the Hilbert transform of the derivatives of the parallel projections. The last example leads necessary to the Hilbert transform. In the first case we can use other transforms to obtain the sought information. Sometimes this is desirable, because the Hilbert transform possess principal directions and a consequence of this property are distorted images. The reduction of this handicap and of whatever kind other interesting results can be created with other integral transforms, is object of the following discourse.