Faculty Publications
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Item Steganalysis: Using the blind deconvolution to retrieve the hidden data(2011) Jidesh, P.; George, S.Steganography has gained a substantial attention due to its application in wide areas. Steganography as it literally mean is hiding the information (stego data) inside the data (communication data) so that the receiver can only extract the desired information from the data. Steganalysis is the reverse process of steganography in which the information about the original data is hardly available, from the received data the extractor needs to identify the original data. Since this belong to a class of inverse problems it is hard to find the approximate match of the original data from the received one. In most of the cases this will fall under the category of ill-posed problems. The stego-data that has been embedded into the communication data can be considered as linear bounded operator operating on the input data and the reverse process (the Steganalysis) can be thought like a deconvolution problem by which we can extract the original data. Here we are assuming the watermarking as a linear operation with a bounded linear operator K : X→Y where X and Y are spaces of Bounded Variation (BV). The forward problem (the Steganography) is a direct convolution and the reverse (backward) problem (steganalysis) is a de-convolution procedure. In this work we are embedding a Gaussian random variable array with zero mean and with a specific variance into the data and we show how the original data can be extracted using the regularization method. The results are shown to substantiate the ability of the method to perform steganalysis. © 2011 IEEE.Item Finite dimensional realization of a Guass-Newton method for ill-posed hammerstein type operator equations(2012) Erappa, M.E.; George, S.Finite dimensional realization of an iterative regularization method for approximately solving the non-linear ill-posed Hammerstein type operator equations KF(x) = f, is considered. The proposed method is a combination of the Tikhonov regularization and Guass-Newton method. The advantage of the proposed method is that, we use the Fr chet derivative of F only at one point in each iteration. We derive the error estimate under a general source condition and the regularization parameter is chosen according to balancing principle of Pereverzev and Schock (2005). The derived error estimate is of optimal order and the numerical example provided proves the efficiency of the proposed method. © 2012 Springer-Verlag.Item Projection method for newton-tikhonov regularization for non-linear ill-posed hammerstein type operator equations(2013) Erappa, M.E.; George, S.An iteratively regularized projection scheme for the ill-posed Hammerstein type operator equation KF(x) = f has been considered. Here F : D(F)X X is a non-linear operator, K : X ? Y is a bounded linear operator, X and Y are Hilbert spaces. The method is a combination of dis- cretized Tikhonov regularization and modified Newton's method. It is assumed that the F?echet derivative of F at x0 is invertible i.e., the ill-posedness of the operator KF is due to the ill-posedness of the linear operator K. Here x0 is an initial approximation to the solution x of KF(x) = f. Adaptive choice of the parameter suggested by Perverzev and Schock(2005) is employed in select- ing the regularization parameter ?. A numerical example is given to test the reliability of the method. © 2013 Academic Publications, Ltd.Item Cubic convergence order yielding iterative regularization methods for ill-posed Hammerstein type operator equations(Springer-Verlag Italia s.r.l. springer@springer.it, 2017) Argyros, I.K.; George, S.; Erappa, S.M.For the solution of nonlinear ill-posed problems, a Two Step Newton-Tikhonov methodology is proposed. Two implementations are discussed and applied to nonlinear ill-posed Hammerstein type operator equations KF(x) = y, where K defines the integral operator and F the function of the solution x on which K operates. In the first case, the Fre´ chet derivative of F is invertible in a neighbourhood which includes the initial guess x0 and the solution x^. In the second case, F is monotone. For both cases, local cubic convergence is established and order optimal error bounds are obtained by choosing the regularization parameter according to the the balancing principle of Pereverzev and Schock (2005).We also present the results of computational experiments giving the evidence of the reliability of our approach. © 2016, Springer-Verlag Italia.