An implicit method for data prediction and impulse noise removal from corrupted signals

A robust and reliable implicit method is proposed for application in data interpolation. The algorithm is based on a recently developed analytic approximation method, namely the distributed approximating functionals (DAFs), which is known to have the "well-tempered" property of UNIFORMLY approximating a function and its derivatives. In comparison with the conventionally used local explicit interpolation algorithms, the implicit method achieves much more accurate interpolation results because it couples all sample values (both known and unknown) in the domain of interest using a set of simultaneous linear algebraic equations. Due to the fact that the well-tempered DAFs also are very good low-pass filters, the performance of the DAF-based implicit method is not affected very much by the high frequency noise in the input signal. As an application, the proposed algorithm is applied to signals that axe corrupted with impulse noise.