Deblurring by a local extrapolation scheme

A special deconvolution problem, where a parameter describes the degree of additive blurring, is considered. No a priori knowledge on the unblurred da ta is assumed. A standard solution based on the output least-squares formul ation includes a regularization parameter into a linear, shift-invariant fi lter An alternative approach that takes advantage of the analyticity of the smoothing process with respect to the blurring parameter is introduced. He re a simple local extrapolation scheme is employed. The problem is encounte red in applications involving potential theories dealing with magnetostatic s, electrostatics and gravity data. Inverse diffraction of scalar waves is also discussed. Examples are presented and the two methods compared numeric ally.