The Research Of Digital Watermarking Based On Fractional Discrete Tchebichef Transform

Image transform has been a hot topic in the application of orthogonal polynomial for a long time,and image security is an important part of image transform.Orthogonal polynomials are widely used in the field of image security because they not only have the characteristics of de-correlation and fast iteration,but also have the property of accurate calculation.Image security including digital watermarking,image encryption and copy-moved,etc.In addition,moments are powerful tool for characterizing image so it can be used for image reconstruction.The proposal of fractional theory actually means that the range of discrete points was enlarged.the fractional discrete Tchebichef transform(Fr DTT)which was a combination of fractional-order and Tchebichef orthogonal transform construct a complete spectral space,and allows discrete Tchebichef orthogonal transform to become an excellent image transform.The main work in this thesis is divided into three aspects:1.After study the mathematical model of orthogonal polynomials,Tchebichef polynomial is selected as the main object to study orthogonal polynomial.According to the definition,properties and characteristics of eigenvalue distribution of Tchebichef polynomial,eigenvalues and eigenvectors of Fr DTT are obtained by eigendecomposition.By modifying the eigenvalues,a basic model of fractional discrete Tchebichef transform is obtained.Moreover,the properties and diversity sequences of fractional discrete Tchebichef transform are also given and analyzed.2.A digital watermarking algorithm based on fractional discrete Tchebichef transform(Fr DTT)is proposed.First,divide the original image into fixed small blocks,then each block was transformed into Fr DTT domain,after the watermark is embed into the host image in the transform domain by dither modulation,and finally by inverse fractional discrete Tchebichef transform(i Fr DTT)obtain a watermarking image which is embedded with watermark information.When need to verify copyright,the watermark is extracted by the minimum distance decoder.By selecting the appropriate fractional coefficients,the image embedded watermark has better imperceptibility and robustness,so the transmission of watermark is more security.In addition,the fractional coefficients can be used as an additional key for the watermark embedding algorithm,which make it spend more time for attackers to crack the information of watermark.3.In order to explore the potential and study description ability of fractional discrete Tchebichef transform in the field of image security,an image encryption algorithm and an image reconstruction algorithm based on fractional discrete Tchebichef transform are both proposed.The sequence generated by the two-dimensional chaotic map as key1 and the generated fractional vector as key2 are used to encrypt image.The introduction of the fractional order further expands the key space and provides a certain guarantee for image security.Image reconstruction is by using as few order of Tchebichef moments as possible to reconstruct image,so as to achieve the purpose that there is little difference between reconstructed image and original image.Experimental results show that under the noise attack,the anti-noise performance of reconstructed image using Fr DTT is better than DTT.