Progressive transmission of secured images with authentication using decompositions into monovariate functions

Abstract

We propose a progressive transmission approach of an image authenticated using an overlapping subimage that can be removed to restore the original image. Our approach is different from most visible watermarking approaches that allow one to later remove the watermark, because the mark is not directly introduced in the two-dimensional image space. Instead, it is rather applied to an equivalent monovariate representation of the image. Precisely, the approach is based on our progressive transmission approach that relies on a modified Kolmogorov spline network, and therefore inherits its advantages: resilience to packet losses during transmission and support of heterogeneous display environments. The marked image can be accessed at any intermediate resolution, and a key is needed to remove the mark to fully recover the original image without loss. Moreover, the key can be different for every resolution, and the images can be globally restored in case of packet losses during the transmission. Our contributions lie in the proposition of decomposing a mark (an overlapping image) and an image into monovariate functions following the Kolmogorov superposition theorem; and in the combination of these monovariate functions to provide a removable visible “watermarking” of images with the ability to restore the original image using a key.