Sphere-hardening Dither Modulation

Spread-Transform Dither Modulation (STDM) is a side-informed data hiding method based on the quantization of a linear projection of the host signal. This projection affords a signal to noise ratio gain which is exploited by Dither Modulation (DM) in the projected domain. Similarly, it is possible to use to the same end the signal to noise ratio gain afforded by the so-called sphere-hardening effect on the norm of a vector. In this paper we describe the Sphere-hardening Dither Modulation (SHDM) data hiding method, which is based on the application of DM to the magnitude of a host signal vector, and we give an analysis of its characteristics. It shown that, in the same sense as STDM can be deemed to be the side-informed counterpart of additive spread spectrum (SS) with repetition coding, SHDM is the side-informed counterpart of multiplicative SS with repetition. Indeed, we demonstrate that SHDM performs similarly as STDM in front of additive independent distortions, but with the particularity that this is achieved through different quantization regions. The quantization hyperplanes which characterize STDM are replaced by quantization spheres in SHDM. The issue of securing SHDM is also studied.