Improved Image Compression Using Bounded-Error Parameter Estimation Concepts

Abstract

Classical approaches to parameter estimation yield point estimates of parameters by optimizing some criterion of fit. In contrast, bounded error parameter estimation (BEPE) methods provide sets of parameters which are consistent with the model structure, observation record, and uncertainty constraints. In general, no knowledge of the statistics of the model or observation uncertainty is assumed. The uncertainty, however, is assumed to be constrained in some manner, e.g., with bounded energy or bounded magnitude.⁽¹⁾ BEPE methods seem more appropriate than classical techniques in several situations. If the actual system is only loosely modeled by the chosen model, it appears more reasonable to attempt to optimize the model so as to bound the model mismatch error, rather than to do classical parameter estimation with erroneous assumptions on the statistics of the model mismatch error. In other cases, the statistics of the observation uncertainty may not be known and BEPE techniques may be effective.