ORIGINAL ARTICLE Robust image watermarking scheme in lifting wavelet domain using GA-LSVR hybridization Rajesh Mehta • Navin Rajpal • Virendra P. Vishwakarma Received: 15 July 2014 / Accepted: 5 January 2015 Ó Springer-Verlag Berlin Heidelberg 2015 Abstract This paper presents an imperceptible, robust, secure and efficient image watermarking scheme in lifting wavelet domain using combination of genetic algorithm (GA) and Lagrangian support vector regression (LSVR). First, four subbands low–low (LL), low–high (LH), high– low (HL) and high–high (HH) are obtained by decompos- ing the host image from spatial domain to frequency domain using one level lifting wavelet transform. Second, the approximate image (LL subband) is divided into non overlapping blocks and the selected blocks based on the fuzzy entropy are used to embed the binary watermark. Third, based on the correlation property of each trans- formed selected block, significant lifting wavelet coeffi- cient act as target to LSVR and its neighboring coefficients (called feature vector) are set as input to LSVR to find optimal regression function. This optimal regression function is used to embed and extract the scrambled watermark. In the proposed scheme, GA is used to solve the problem of optimal watermark embedding strength, based on the noise sensitivity of each selected block, in order to increase the imperceptibility of the watermark. Due to the good learning capability and high generalization property of LSVR against noisy datasets, high degree of robustness is achieved and is well suited for copyright protection applications. Experimental results on standard and real world images show that proposed scheme not only efficient in terms of computational cost and memory requirement but also achieve good imperceptibility and robustness against geometric and non geometric attacks like JPEG compression, median filtering, average filtering, addition of noise, sharpening, scaling, cropping and rota- tion compared with the state-of-art techniques. Keywords Fuzzy entropy  Genetic algorithm  Lagrangian support vector regression  Lifting wavelet transform 1 Introduction Day by day popularization of multimedia and network technologies, ownership of multimedia data, illegal copy- ing, avoiding duplicity and copyright protection has become the challenging issues. Digital watermarking (audio, video and image) [7, 10, 11] provides a solution to all these problems. This is the process of embedding the watermark in the host signal in an imperceptible manner [7, 28, 36]. Imperceptibility, robustness, security and payload are the main requirements of any watermarking scheme [7, 10, 11, 28]. Based on the domain analysis, watermarking schemes are divided into two categories; spatial domain schemes and transform domain schemes. In spatial domain schemes, the pixels value of the host image is directly modified during watermark embedding [28, 36]. Modifying the least significant bits (LSBs) of the pixel value of the host image by the watermark bit is the easiest method to embed the watermark [28]. The main feature of spatial domain methods is of its easy implementation and imper- ceptibility but these methods are less robust to geometric and non geometric image processing attacks. In transform R. Mehta (&)  N. Rajpal  V. P. Vishwakarma University School of Information and Communication Technology, Guru Gobind Singh Indraprastha University, Sector 16-C, New Delhi, India e-mail: rajesh2010usit@gmail.com N. Rajpal e-mail: navin_rajpal@yahoo.com V. P. Vishwakarma e-mail: virendravishwa@rediffmail.com 123 Int. J. Mach. Learn. & Cyber. DOI 10.1007/s13042-015-0329-6