Optimized Gray-Scale Image Watermarking Algorithm Based on DWT-DCT-SVD and Chaotic Firefly Algorithm

This paper presents an optimized watermarking scheme based on the discrete wavelet transform (DWT), discrete cosine transform (DCT) and singular value decomposition (SVD). The result of multiplying the left singular vector and matrix with the singular value matrix of a binary watermark are embedded in the result of multiplying the left singular vector and matrix and the singular value matrix of the DCT matrix of the LL3 sub-band coefficients of the host image by making use of multiple scaling factors (MSFs). Furthermore, the MSFs are optimized using a newly proposed Chaotic Firefly Algorithm using logistic map having an objective function which is a linear combination of imperceptibility and robustness. The PSNR values of the signed and attacked images indicate that the watermarking scheme has good imperceptibility. The embedding algorithm is robust against eight common image processing operations. It is concluded that the embedding and extraction of the proposed algorithm has good imperceptibility, high security and well robustness after comparing other similar reported methods.