Watermarking Applications of Krawtchouk–Sobolev Type Orthogonal Moments

Abstract

In this contribution, we consider the sequence {Hn ( x; q)}n≥0 of monic polynomials orthogonal with respect to a Sobolev-type inner product involving forward difference operators For the first time in the literature, we apply the non-standard properties of {Hn ( x; q)}n≥0 in a watermarking problem. Several differences are found in this watermarking application for the non-standard cases (when j > 0) with respect to the standard classical Krawtchouk case λ = µ = 0.