Generalized Wiener Filtering Computation Techniques

The classical signal processing technique known as Wiener filtering has been extended to the processing of oneand two-dimensional discrete data by digital operations with emphasis on reduction of the computational requirements. In the generalized Wiener filtering process a unitary transformation, such as the discrete Fourier, Hadamard, or Karhunen-Loeve transform is performed on the data that is assumed to be composed of additive signal and noise components. The transformed data is then modified by a filter function, and the inverse transformation is performed to obtain the discrete system output. The filter function is chosen to provide the best mean square estimate of the signal portion of the input data. It is shown that all unitary data transformations provide the same minimum mean square error performance. However, by using fast transform algorithms, the computational requirements for some of the transforms, e.g., Fourier and Hadamard, can be reduced significantly. Furthermore, with certain data transforms, a selective computational procedure will result in a significant reduction in computation load, with only a minimal increase in estimation error. An example of the application of the generalized Wiener filtering process to image enhancement is presented.