Steganography is the art of hiding high sensitive information in digital image, text, video, and audio. In this paper, authors have proposed a frequency domain steganography method operating in the Ridgelet transform. Authors engage the advantage of ridgelet transform, which represents the digital image with straight edges. In the embedding phase, the proposed hybrid edge detector acts as a preprocessing step to obtain the edge image from the cover image, then the edge image is partitioned into several blocks to operate with straight edges and Ridgelet transform is applied to each block. Then, the most significant gradient vectors (or significant edges) are selected to embed the secret data. The proposed method has shown the advantages of imperceptibility of the stego image is increased because the secret data is hidden in the significant gradient vector. Authors employed the hybrid edge detector to obtain the edge image, which increases the embedding capacity. Experimental results demonstrates that peak signal-to-noise (PSNR) ratio of stego image generated by this method versus the cover image is guaranteed to be above 49 dB. PSNR is much higher than that of all data hiding techniques reported in the literature.Keywords: Steganography, data hiding, information security, ridgelet transform, hybrid edge detector MAHeSwARI & HeMANTH : IMAge STegANogRAPHy USINg HyBRID eDge DeTeCToR AND RIDgeLeT TRANSfoRM 215 processing step, the authors force to extract the edge image by sending the cover image to the hybrid edge detector domain. After that, the edge image is partitioned into several blocks in which the ridgelet transform is applied to each block. Then, the most significant gradient vectors are selected to hide the secret data. finally, inverse ridgelet transform is applied to obtain the stego image.
rIdgElEt trAnSform 2.1 continuous ridgelet transformThe continuous ridgelet transform was proposed by Candes and Donoho 12 . given a 1-D wavelet transform which indicate the element (.)where ( ,b θ ) are line parameter and a>0 is a scale parameter. The line parameter cos sin u v b θ+ θ = , known as ridgelets. The continuous ridgelet transform (CRT) for given functionIts inverse formula is given by Starck 13 , et al.from eqns (2) and (3), CRT is calculated by applying wavelet transform in the radon transform. The radon domain equation is given by 2 ( , ) ( , ) ( cos sin )where δ is the dirac function. To obtain the RT, 1-D wavelet transform is applied to the radon transform which is given by 1 2 ( , , ) ( , ) ( )where θ is constant and t is variant. Thus, to obtain the fast RT, the fourier domain is introduced. The 2-D-ffT is applied to the input image, then the 1-D inverse ffT is applied to the radon transform. finally, the 1-D wavelet transform is applied to radon transform to obtain the ridgelet coefficients.
finite ridgelet transformThe finite ridgelet transform was developed from the finite radon transform as shown in fig 1. The finite radon transform of a real function (C) defined as a 2-D grid 2 p Z is g...