MINIMUM-VARIANCE DECONVOLUTION FOR NONCAUSAL WAVELETS

Deconvolution is an important technique in data processing. At present , there have been a lot of publications on deconvolution problems. Mos t of them are only applicable to causal wavelets. In this paper the mi nimum-variance deconvolution for noncausal wavelets are studied. First , an equivalent recursive model to the convolutional sum model for non causal wavelets is set up. This recursive model is a descriptor model with two-point boundary conditions. Second, using the estimation theor y of two-point boundary value systems, the minimum-variance estimator of input or reflection is presented and the corresponding implementati on procedures of the input estimator and the estimation error variance are derived. Finally, examples are provided that illustrate the perfo rmance of the algorithms in this paper.