Faculty Publications

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Publications by NITK Faculty

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Author: search.filters.author.Padikkal, J.Has files: No

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    On the convergence of Homeier method and its extensions
    (Springer Science and Business Media B.V., 2022) Muhammed Saeed, K.; Krishnendu, R.; George, S.; Padikkal, J.
    A third-order Homeier method for solving equations in Banach space is studied. Using assumptions on the first and second derivatives, we obtained third-order convergence. Our technique does not involve Taylor series expansion and can be extended to similar higher-order methods. We have given two extensions of the method with orders five and six. Examples with radii of convergence and basins of attraction are provided. © 2022, The Author(s), under exclusive licence to The Forum D’Analystes.
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    Finite dimensional realization of fractional Tikhonov regularization method in Hilbert scales
    (Elsevier B.V., 2022) Mekoth, C.; George, S.; Padikkal, J.; Erappa, S.M.
    One of the intuitive restrictions of infinite dimensional Fractional Tikhonov Regularization Method (FTRM) for ill-posed operator equations is its numerical realization. This paper addresses the issue to a considerable extent by using its finite dimensional realization in the setting of Hilbert scales. Using adaptive parameter choice strategy, we choose the regularization parameter and obtain an optimal order error estimate. Also, the proposed method is applied to the well known examples in the setting of Hilbert scales. © 2021 The Author(s)
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    Detection of retinal disorders from OCT images using generative adversarial networks
    (Springer, 2022) Smitha, A.; Padikkal, J.
    Retinal image analysis has opened up a new window for prompt diagnosis and detection of various retinal disorders. Optical Coherence Tomography (OCT) is one of the major diagnostic tools to identify retinal abnormalities related to macular disorders like Age-Related Macular Degeneration (AMD) and Diabetic Macular Edema (DME). The clinical findings include retinal layer analysis to spot the abnormalities on OCT images. Though various models are proposed over the years to diagnose these disorders automatically, an end-to-end system that performs automatic denoising, segmentation, and classification does not exist to the best of our knowledge. This paper proposes a Generative Adversarial Network (GAN) based approach for automated segmentation and classification of OCT-B scans to diagnose AMD and DME. The proposed method incorporates the integration of handcrafted Gabor features to enhance the retina layer segmentation and non-local denoising to remove speckle noise. The classification metrics of GAN are compared with existing methods. The accuracy of up to 92.42% and F1-score of 0.79 indicates that the GANs can perform well for segmentation and classification of OCT images. © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
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    A New Parameter Choice Strategy for Lavrentiev Regularization Method for Nonlinear Ill-Posed Equations
    (MDPI, 2022) George, S.; Padikkal, J.; Remesh, K.; Argyros, I.K.
    In this paper, we introduced a new source condition and a new parameter-choice strategy which also gives the known best error estimate. To obtain the results we used the assumptions used in earlier studies. Further, we studied the proposed new parameter-choice strategy and applied it to the method (in the finite-dimensional setting) considered in George and Nair (2017). © 2022 by the authors.
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    On Newton’s Midpoint-Type Iterative Scheme’s Convergence
    (Springer, 2022) Krishnendu, R.; Saeed, M.; George, S.; Padikkal, J.
    This paper introduce new three step iterative schemes with order of convergence five and six for solving nonlinear equations in Banach spaces. The proposed scheme’s convergence is assessed using assumptions on the operator’s derivatives up to order two. Unlike earlier studies, the convergence study of these methods are not based on the Taylor’s expansion. Numerical examples and Basin of attractions are given in this study © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.
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    Restoration and Enhancement of Aerial and Synthetic Aperture Radar Images Using Generative Deep Image Prior Architecture
    (Springer Science and Business Media Deutschland GmbH, 2022) Shastry, A.; Smitha, A.; George, S.; Padikkal, J.
    Restoration and enhancement of low light images is an inevitable pre-processing activity among remote sensing, aerial and satellite imaging modalities. The images captured under various atmospheric conditions are distorted. Therefore, they need a thorough conditioning before being analysed. In this paper, we propose a retinex-based variational framework designed under a generative deep image prior architecture to restore and enhance distorted images from satellite, aerial and remote sensing applications. The model handles data-correlated speckle noise found in active image sensing modalities, duly considering its distribution. The data-fidelity aspect of the proposed variational framework is designed using the Bayesian Maximum A Posteriori (MAP) estimate, assuming that the input images are contaminated with Gamma distributed speckled interference. Further, model is catered to handle various noise distributions, such as Gaussian and Poisson, by appropriately altering the data fidelity term specific to the distribution, without modifying the architecture of the model. The variational retinex model employed herein also addresses contrast degradation and intensity inhomogeneity aberrations in the input images. The proposed model is assessed qualitatively using visual comparisons and quantified using the relevant statistical measures. The experimental results confirm that the proposed model outperforms the existing methods in terms of restoration and contrast enhancement of speckled images. The proposed method also has shown the full potential to adapt the model to restore the degraded images following any distribution. © 2022, Deutsche Gesellschaft für Photogrammetrie, Fernerkundung und Geoinformation (DGPF) e.V.
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    On the Order of Convergence of the Noor–Waseem Method
    (MDPI, 2022) George, S.; Sadananda, R.; Padikkal, J.; Argyros, I.K.
    In 2009, Noor and Waseem studied an important third-order iterative method. The convergenceorder is obtained using Taylor expansion and assumptions on the derivatives of order up tofour. In this paper, we have obtained convergence order three for this method using assumptionson the first and second derivatives of the involved operator. Further, we have extended the methodto obtain a fifth- and a sixth-order methods. The dynamics of the methods are also provided in thisstudy. Numerical examples are included. The same technique can be used to extend the utilization ofother single or multistep methods. © 2022 by the authors.
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    Extending the Applicability of Cordero Type Iterative Method
    (MDPI, 2022) Remesh, K.; Argyros, I.K.; Saeed, M.; George, S.; Padikkal, J.
    Symmetries play a vital role in the study of physical systems. For example, microworld and quantum physics problems are modeled on the principles of symmetry. These problems are then formulated as equations defined on suitable abstract spaces. Most of these studies reduce to solving nonlinear equations in suitable abstract spaces iteratively. In particular, the convergence of a sixth-order Cordero type iterative method for solving nonlinear equations was studied using Taylor expansion and assumptions on the derivatives of order up to six. In this study, we obtained order of convergence six for Cordero type method using assumptions only on the first derivative. Moreover, we modified Cordero’s method and obtained an eighth-order iterative scheme. Further, we considered analogous iterative methods to solve an ill-posed problem in a Hilbert space setting. © 2022 by the authors.
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    An apriori parameter choice strategy and a fifth order iterative scheme for Lavrentiev regularization method
    (Institute for Ionics, 2023) George, S.; Saeed, M.; Argyros, I.K.; Padikkal, J.
    In this paper, we propose a new source condition and introduce a new apriori parameter choice strategy for Lavrentiev regularization method for nonlinear ill-posed operator equation involving a monotone operator in the setting of a Hilbert space. Also, a fifth order iterative method is being proposed for approximately solving Lavrentiev regularized equation. A numerical example is illustrated to demonstrate the performance of the method. © 2022, The Author(s) under exclusive licence to Korean Society for Informatics and Computational Applied Mathematics.
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    Order of Convergence and Dynamics of Newton–Gauss-Type Methods
    (MDPI, 2023) Sadananda, R.; George, S.; Argyros, I.K.; Padikkal, J.
    On the basis of the new iterative technique designed by Zhongli Liu in 2016 with convergence orders of three and five, an extension to order six can be found in this paper. The study of high-convergence-order iterative methods under weak conditions is of extreme importance, because higher order means that fewer iterations are carried out to achieve a predetermined error tolerance. In order to enhance the practicality of these methods by Zhongli Liu, the convergence analysis is carried out without the application of Taylor expansion and requires the operator to be only two times differentiable, unlike the earlier studies. A semilocal convergence analysis is provided. Furthermore, numerical experiments verifying the convergence criteria, comparative studies and the dynamics are discussed for better interpretation. © 2023 by the authors.