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. Most of them are only applicable to causal wavelets. In this paper the minimum-variance deconvolution for noncausal wavelets are studied. First, an equivalent recursive model to the convolutional sum model for noncausal wavelets is set up. This recursive model is a descriptor model with two-point boundary conditions. Second, using the estimation theory of two-point boundary value systems, the minimum-variance estimator of input or reflection is presented and the corresponding implementation procedures of the input estimator and the estimation error variance are derived. Finally, examples are provided that illustrate the performance of the algorithms in this paper