Decon comparisons between Burg and conjugate-gradient methods

INTRODUCTION

The classical stationary linear least-squares deconvolution problem may be solved in a variety of ways. While testing our new sparseness deconvolution method (non-causal, non-linear, hyperbolic penalty) we had occasion to use some classic methods for comparisons. In particular, we used the Burg decon code (Claerbout, 1976) and the conjugate direction (CD) code (Pef in Claerbout and Fomel (2012)). In the absence of precision issues, the CD code is theoretically equivalent to the conjugate gradient method. Unexpectedly, during our early studies some astonishing differences appeared. Were these differences due to coding bugs, improper comparisons, or precision issues not previously recognized by us? Perhaps all. These two methods do differ in some fundamental aspects, principally but not entirely related to end effects. Another difference is that the Burg method assures a minimum-phase filter but that is not true of the regression methods in GEE, namely Pef.