A method is presented for decoding an encoded image produced from a primary image and at least one secondary image using at least one encoding parameter. The encoded image is formed so that when the encoded image is printed, the secondary image is not discernible to a viewer without an optical decoding device having characteristics corresponding to the at least one encoding parameter. The method comprises obtaining a digital version of the encoded image, determining the at least one encoding parameter, and constructing a decoded image from the digital encoded image using at least one of the encoding parameters in the encoding parameter set.