Faculty Publications
Permanent URI for this communityhttps://idr.nitk.ac.in/handle/123456789/18736
Publications by NITK Faculty
Browse
10 results
Search Results
Item Inverse modeling of heat transfer with application to solidification and quenching(2002) Prabhu, K.N.; Ashish, A.A.The inverse modeling of heat transfer involves the estimation of boundary conditions from the knowledge of thermal history inside a heat conducting body. Inverse analysis is extremely useful in modeling of contact heat transfer at interfaces of engineering surface during materials processing. In the present work, the one-dimensional transient heat conduction equation was inversely modeled in both cartesian as well as cylindrical coordinates. The model is capable of estimating heat flux transients, chill surface temperature, and total heat flow from the source to the sink for an input of thermal history inside the sink. The methodology was adopted to solve boundary heat transfer problems inversely during solidification and quenching. The response of the inverse solution to measured sensor data was studied by carrying out numerical experiments involving the use of varying grid size and time steps, future temperatures, and regularization techniques.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 Non-local Gradient Fidelity Model for Multiplicative Gamma Noise Removal(Institute of Electrical and Electronics Engineers Inc., 2018) Banothu, B.; Jidesh, P.In this paper a non-local gradient vector flow model is designed for restoration of images corrupted with Gamma distributed (speckle) noise and linear blurring artefacts. The filter effectively preserves edges and finer details in the course of its evolution due to the presence of the non-local TV based diffusion term and the piecewise linear approximation is reduced considerably by the gradient fidelity term present in the model. The model is found suitable for restoration of various images from the field of satellite and clinical imaging. The experimental results are shown and compared for different image data sets both visually and qualitatively using various statistical measures. © 2017 IEEE.Item A Graph Spectral Approach for Restoring Images Corrupted by Shot-Noise(Springer Science and Business Media Deutschland GmbH, 2021) Jidesh, P.; Bini, A.A.Image restoration is a fundamental problem in image processing. Usually, images gets deteriorated while storing or transmitting them. Image restoration is an ill-posed inverse problem, wherein one has to restore the original data with a priori information or assumption regarding the degradation model and its characteristics. The literature is too elaborate for various restorations under different assumptions on the degradation-architecture. This paper introduces a strategy based on graph spectral theory to restore images with non-local filters controlled by a loss function. The non-local similarity-based weight function controls the restoration process resulting in the preservation of local image features considerably well. The parameter controlled adaptive fidelity term helps to re-orient the diffusion to handle data correlated shot-noise following a Poisson distribution, which is pretty common in many medical and telescopic imaging applications. Experimental results are conforming to the fact that the proposed model performs well in restoring images of the different intensity distributions. © 2021, Springer Nature Singapore Pte Ltd.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 A nonlinear level set model for image deblurring and denoising(Springer Verlag service@springer.de, 2014) Bini, A.A.; Bhat, M.S.Image deblurring and denoising are fundamental problems in the field of image processing with numerous applications. This paper presents a new nonlinear Partial Differential Equation (PDE) model based on curve evolution via level sets, for recovering images from their blurry and noisy observations. The proposed method integrates an image deconvolution process and a curve evolution based regularizing process to form a reaction-diffusion PDE. The regularization term in the proposed PDE is a combination of a diffusive image smoothing term and a reactive image enhancement term. The diffusive and reactive terms present in the model lead to effective suppression of noise with sharp restoration of image features. We present several numerical results for image restoration, with synthetic and real degradations and compare it to other state-of-the-art image restoration techniques. The experiments confirm the favorable performance of our method, both visually and in terms of Improvement in Signal-to-Noise-Ratio (ISNR) and Pratt's Figure Of Merit (FOM). © 2013 Springer-Verlag Berlin Heidelberg.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.Item Image despeckling with non-local total bounded variation regularization(Elsevier Ltd, 2018) Padikkal, P.; Banothu, B.A non-local total bounded variational (TBV) regularization model is proposed for restoring images corrupted with data-correlated speckles and linear blurring artifacts. The energy functional of the model is derived using maximum a posteriori (MAP) estimate of the noise probability density function (PDF). The non-local total bounded variation prior regularizes the model while the data fidelity is derived using the MAP estimator of the noise PDF. The computational efficiency of the model is improved using a fast numerical scheme based on the Augmented Lagrange formulation. The proposed model is employed to restore ultrasound (US) and synthetic aperture radar (SAR) images, which are usually speckled and blurred. The numerical results are presented and compared. Furthermore, a detailed theoretical study of the model is performed in addition to the experimental analysis. © 2017 Elsevier LtdItem Estimation of Noise Using Non-local Regularization Frameworks for Image Denoising and Analysis(Springer Verlag, 2019) Padikkal, P.; Febin, I.P.In this paper, we propose a novel model which adaptively estimates the noise probability distribution and noise parameters from the input image and restores the data accordingly choosing appropriate regularization model designed for it. In most imaging applications the noise characteristics are assumed prior to the restoration process. This assumption is generally based on the previous experimental study of the images from a specific modality. The adaptive detection of the noise distribution from the data makes it robust and highly suitable for automated signal and image restoration systems. The non-local framework implemented using fast numerical solvers catalyzes the convergence rate of the model. Here we analyze three different noise distributions such as Gamma, Poisson, and Gaussian. Among this Gaussian is additive and source independent, Gamma is multiplicative and source dependent, and finally Poisson is data dependent (neither multiplicative nor additive). The model can be extended to the other source-dependent distributions such as Rayleigh and Rician by appropriately tuning it. The experimental results conform to the assumption regarding the noise distribution and noise parameters estimation capability of the model. © 2018, King Fahd University of Petroleum & Minerals.