l1-optimal deconvolution with stable predictor polynomials

The problem of l₁-optimal deconvolution with stable predictor polynomials is addressed. It is shown that the problem of l₁ deconvolution can be formulated as a standard model-matching problem that can be solved using some results from the literature. The authors consider how to stabilize the resulting predictor polynomial in the event that it is unstable. Two equivalent existence conditions which indicate when it is possible to stabilize the predictor are presented. The Nehari theorem is then used to give a procedure to find a filter whose first M coefficients match those of the l₁-optimal filter, but which will exhibit a stable predictor polynomial