Browsing by Author "Padikkal, P."

Now showing 1 - 20 of 48

A convex regularization model for image restoration
(Elsevier Ltd, 2014) Padikkal, P.
Many variational formulations are introduced over the last few years to handle multiplicative data-dependent noise. Some of these models seek to minimize the Total Variation (TV) norm of the absolute gradient function subject to given constraints. Since the TV-norm (well-defined in the space of bounded variations (BVs)) minimization eventually results in the formation of piece-wise constant patches during the evolution process, the filtered output appears blocky. In this work the block effect (commonly known as staircase effect) is being handled by using a convex combination of TV and Tikhonov filters, which are defined in BV and L2 (square-integrable functions) spaces, respectively. The constraint for the minimizing functional is derived based on a maximum a posteriori (MAP) regularization approach, duly considering the noise distributions. Therefore, this model is capable of denoising speckled images, whose intensity is Gamma distributed. The results are demonstrated both in terms of visual and quantitative measures. © 2014 Elsevier Ltd. All rights reserved.
A Curvature-Driven Image Inpainting Approach for High-Density Impulse Noise Removal
(Springer Verlag, 2014) Padikkal, P.; Bini, A.A.
A PDE-based image inpainting method is proposed in this work for removing high-density impulse noise in images. In this model, the diffusion or inpainting process is driven by the difference curvature of the level curve. The proposed framework has two stages. In the first stage the noisy pixels are detected and they are piped to the second stage. In the second stage, these noisy pixels are inpainted using the information from their neighborhood. The connectivity principle is well realized and the edges and fine details are preserved well by the proposed model. The proposed method is compared (in terms of denoising capability) with the state-of-the-art impulse denoising models. The performance is quantified in terms of statistical quality measures. It is observed that the proposed method is capable of restoring images corrupted with high-density impulse noise (even up to 90 %). The experiments clearly demonstrate the effective restoration capacity of the proposed image inpainting model. © 2014 King Fahd University of Petroleum and Minerals.
A derivative free iterative method for the implementation of Lavrentiev regularization method for ill-posed equations
(Kluwer Academic Publishers, 2015) Shubha, V.S.; George, S.; Padikkal, P.
In this work, we develop a derivative free iterative method for the implementation of Lavrentiev regularization for approximately solving the nonlinear ill-posed operator equation F(x) = y. Convergence analysis shows that the method converges quadratically. Apart from being totally free of derivatives, the method, under a general source condition provide an optimal order error estimate. We use the adaptive method introduced in Pereverzyev and Schock (SIAM J. Numer. Anal. 43, 2060–2076, 2005) for choosing the regularization parameter. In the concluding section the method is applied to numerical solution of the inverse gravimetry problem. © 2014, Springer Science+Business Media New York.
A fully-automated system for identification and classification of subsolid nodules in lung computed tomographic scans
(Elsevier Ltd, 2019) Savitha, G.; Padikkal, P.
A fully-automated computer-aided detection (CAD) system is being proposed in this paper for identification and classification of subsolid lung nodules present in Computed Tomography(CT) scans. The system consists of two stages. The first stage aims at detecting locations of the nodules, while the second one classifies the same into the solid and subsolid category. The system performs segmentation of the region of interest (ROI) and extraction of relevant features from the segmented ROI. Graylevel covariance matrix (GLCM) is being used to extract the Feature vectors. Principle component analysis (PCA) algorithm is used to select significant features in the feature space formed by the vectors. The nodule localization is performed using support vector machine, fuzzy C-means, and random forest classification algorithms. The identified nodules are further grouped into solid and subsolid nodules by extracting histogram of gradient (HoG) features adopting K-means and support vector machine (SVM) classifiers. A large number of annotated images from the widely available benchmark database is tested to validate the results. Efficiency and reliability of the system are evaluated visually and numerically using the relevant quantitative measures. The developed CAD system is found to identify subsolid nodules with a high percentage of accuracy. © 2019 Elsevier Ltd
A holistic deep learning approach for identification and classification of sub-solid lung nodules in computed tomographic scans
(Elsevier Ltd, 2020) Savitha, G.; Padikkal, P.
Prompt detection of malignant lung nodules significantly improves the chance of survivability of the affected patients. The lung nodules in their early stages appear as subsolid or part-solid nodules whose identification remains a challenging task. Many of the present lung nodule detection systems fail to identify the nodules in their early stages. Limitations in the feature extraction process lead to significant false-positive rates, which eventually diminish the accuracy aspects of the system. In this study, a sophisticated deep learning approach is employed for feature extraction which improves the nodule localization or identification stage of the system. Further, the false positives sneaking out of the system are drastically reduced by adopting a Conditional Random Framework in the model. The quantitative demonstrations prove the efficiency of the model to detect sub-solid nodules in CT images. Thus the employability of the model for early detection of the nodules is tested and verified. © 2020 Elsevier Ltd
A nonlocal deep image prior model to restore optical coherence tomographic images from gamma distributed speckle noise
(Taylor and Francis Ltd., 2021) Smitha, A.; Padikkal, P.
Optical Coherence Tomography (OCT) is often employed to observe the retinal layers in the human eyes. The retinal scans are susceptible to artefacts such as head movements or eye blinks. Along with this, the quality of the images is degraded by speckle noise caused due to the constructive and destructive interference of the waves used for capturing data. Recently, image restoration techniques have geared up in terms of quality with the exertion of deep learning. Despeckling using deep learning, in general, necessitates a large set of training images. On the contrary, deep image prior is a novel model that performs denoising operations using a single training image, based on a prior assumption about the noise distribution. This paper extends the concept of the deep image prior towards non-local restoration for speckle noise assuming that the speckle follows Gamma distribution. Such a framework can be incorporated to enhance the OCT images. The proposed framework is assessed qualitatively with visual comparisons and quantitatively using statistical measures like PSNR, CNR and ENL. Comparative studies confirm that the proposed method outperforms the existing methods in restoring speckled input images. © 2021 Informa UK Limited, trading as Taylor & Francis Group.
A Perceptually Inspired Variational Model for Enhancing and Restoring Remote Sensing Images
(Institute of Electrical and Electronics Engineers Inc., 2021) Padikkal, P.; Febin, I.P.
Perceptually inspired algorithms have captured the recent attention of scientists and engineers due to their inherent capability to enhance the contrast of images, especially from the remote sensing domain. In this letter, we propose a perceptually inspired retinex model relying on the variational framework for enhancing and denoising satellite images captured by various imaging devices. A variational framework incorporates priors and data fidelity aspects in the designed functional, whose optimized solution yields the desired output. The model respects the distribution of the noise while enhancing the data. The overall performance is demonstrated using the visual and quantitative measures. © 2004-2012 IEEE.
A quadratic convergence yielding iterative method for the implementation of Lavrentiev regularization method for ill-posed equations
(Elsevier Inc. usjcs@elsevier.com, 2015) Padikkal, P.; Shubha, V.S.; George, S.
George and Elmahdy (2012), considered an iterative method which converges quadratically to the unique solution x?? of the method of Lavrentiev regularization, i.e., F(x) + ?(x - x0) = y?, approximating the solution x of the ill-posed problem F(x) = y where F:D(F)?X?X is a nonlinear monotone operator defined on a real Hilbert space X. The convergence analysis of the method was based on a majorizing sequence. In this paper we are concerned with the problem of expanding the applicability of the method considered by George and Elmahdy (2012) by weakening the restrictive conditions imposed on the radius of the convergence ball and also by weakening the popular Lipschitz-type hypotheses considered in earlier studies such as George and Elmahdy (2012), Mahale and Nair (2009), Mathe and Perverzev (2003), Nair and Ravishankar (2008), Semenova (2010) and Tautanhahn (2002). We show that the adaptive scheme considered by Perverzev and Schock (2005) for choosing the regularization parameter can be effectively used here for obtaining order optimal error estimate. In the concluding section the method is applied to numerical solution of the inverse gravimetry problem. © 2014 Elsevier Inc. All rights reserved.
A retinex based non-local total generalized variation framework for OCT image restoration
(Elsevier Ltd, 2022) Smitha, A.; Febin, I.P.; Padikkal, P.
A retinex driven non-local total generalized variational (TGV) model is proposed in this paper to restore and enhance speckled images. The combined first and second-order TGV controlled by a balancing parameter are used to improve the enhancement and restoration process. The distribution of the speckle is estimated from input images using detailed statistical analysis. The model is designed to handle speckle-noise following a Gamma distribution, as analyzed later in this paper. The non-local TGV model is shown to restore images without causing any visual artefacts, unlike the normal total variation (TV) model. Moreover, a retinex framework shows a remarkable improvement to the contrast features of the data without distorting the natural image characteristics as quantified visually and statistically in the experimental section of this work. A fast numerical approximation based on the Split-Bregman scheme is employed to improve the efficiency of the model in terms of computation. The proposed model is verified to have despeckled and enhanced the Optical Coherence Tomography (OCT) data to a greater extent compared to the state-of-the-art models as observable from the results shown in this paper. © 2021 Elsevier Ltd
A Retinex-Based Variational Model for Enhancement and Restoration of Low-Contrast Remote-Sensed Images Corrupted by Shot Noise
(Institute of Electrical and Electronics Engineers, 2020) Febin, I.P.; Padikkal, P.; Bini, A.A.
Remotely sensed images are widely used in many imaging applications. Images captured under adverse atmospheric conditions lead to degraded images that are contrast deficient and noisy. This study is intended to address these defects of remotely sensed data efficiently. A perceptually inspired variational model is designed based upon the Bayesian framework, powered by the retinex theory. The atmospheric noise or the shot noise (precisely following a Poisson distribution) and contrast inhomogeneity are addressed in this article. The model thus designed is tested and verified both visually and quantitatively using various test data under different statistical measures. The comparative study reveals the efficiency of the model. © 2020 IEEE.
A time-dependent switching anisotropic diffusion model for denoising and deblurring images
(2012) Padikkal, P.; George, S.
A conditionally anisotropic diffusion based deblurring and denoising filter is introduced in this paper. This is a time-dependent curvature based model and the steady state can be attained at a faster rate, using the explicit time-marching scheme. The filter switches between isotropic and anisotropic diffusion depending on the local image features. The switching of the filter is controlled by a binary function, which returns either zero or one, based on the underlying local image gradient features. The parameters in the proposed filter can be fine-tuned to get the desired output image. The filter is applied to various kinds of input test images and the response is analyzed. The filter is found to be effective in the reconstruction of partially textured, textured, constant-intensity and color images, as is evident from the results provided. © 2011 Copyright Taylor and Francis Group, LLC.
Adaptive non-local level-set model for despeckling and deblurring of synthetic aperture radar imagery
(Taylor and Francis Ltd. michael.wagreich@univie.ac.at, 2018) Padikkal, P.; Banothu, B.
In this article, we modify Mumford–Shah level-set model to handle speckles and blur in synthetic aperture radar (SAR) imagery. The proposed model is formulated using a non-local regularization framework. Hence, the model duly cares about local gradient oscillations (corresponding to the fine details/textures) during the evolution process. It is assumed that the speckle intensity is gamma distributed, while designing a maximum a posteriori estimator of the functional. The parameters of the gamma distribution (i.e. scale and shape) are estimated using a maximum likelihood estimator. The regularization parameter of the model is evaluated adaptively using these (estimated) parameters at each iteration. The split-Bregman iterative scheme is employed to improve the convergence rate of the model. The proposed and the state-of-the-art despeckling models are experimentally verified and compared using a large number of speckled and blurred SAR images. Statistical quantifiers are used to numerically evaluate the performance of various models under consideration. © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.
An improved semi-local convergence analysis for a three point method of order 1.839 in banach space
(International Publications internationalpubls@yahoo.com, 2015) Argyros, I.K.; Padikkal, P.; George, S.
We present a new semi-local convergence analysis for a three point method of order 1.839 in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. The advantages of the new approach over earlier ones such as [18] are: weaker and easier to verify convergence conditions. Moreover the radius of convergence is given in an explicit form. Furthermore, uniqueness results are also presented for the first time as far as we know in this paper. Finally, numerical example illustrating the theoretical results is given.
Ball Convergence for Second Derivative Free Methods in Banach Space
(Springer, 2017) Argyros, I.K.; Padikkal, P.; George, S.
Hueso et al. (Appl Math Comput 211:190–197, 2009) considered a third and fourth order iterative methods for nonlinear systems. The methods were shown to of order third and fourth if the operator equation is defined on the j-dimensional Euclidean space (Hueso et al. in Appl Math Comput 211:190–197, 2009). The order of convergence was shown using hypotheses up to the third Fréchet derivative of the operator involved although only the first derivative appears in these methods. In the present study we only use hypotheses on the first Fréchet-derivative. This way the applicability of these methods is expanded. Moreover we present a radius of convergence a uniqueness result and computable error bounds based on Lipschitz constants. Numerical examples are also presented in this study. © 2015, Springer India Pvt. Ltd.
Classification of Multiple Retinal Disorders from Enhanced Fundus Images Using Semi-supervised GAN
(Springer, 2022) Smitha, A.; Padikkal, P.
Automatic detection of retinal disorders is gaining considerable attention with the emergence of deep learning. Ophthalmologists primarily use color fundus photographs to examine the human retina and diagnose the abnormalities. As there is a surge in the number of visual impairments, an AI-enabled retina screening system can expedite the retina examination process. Existing works in this direction are primarily focused on either segmentation or classification. Furthermore, the majority of the works are implemented using preprocessed good quality fundus images. In reality, however, the quality of color fundus images is degraded due to the illumination inhomogeneity and low contrast issues. Thus, there is a need to develop an end-to-end fundus image analysing system. Steering in this direction, the proposed work attempts to analyze the performance of semi-supervised Generative Adversarial Networks (GANs) for the classification of retinal fundus images into multiple categories. Besides, the nonlocal retinex framework is applied to enhance the quality of fundus images without over-smoothing the edges. The large data set of raw fundus acquired from multiple Eye hospitals and released in public domain is used to implement the proposed work. The results obtained are compared with the transfer learning method, and an average accuracy of 87% is obtained. It suggests that the semi-supervised GANs can be potentially used to classify heterogeneous retinal disorders. © The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd 2021.
Convergence Analysis of a Fifth-Order Iterative Method Using Recurrence Relations and Conditions on the First Derivative
(Birkhauser, 2021) George, S.; Argyros, I.K.; Padikkal, P.; Mahapatra, M.; Saeed, M.
Using conditions on the second Fréchet derivative, fifth order of convergence was established in Singh et al. (Mediterr J Math 13:4219–4235, 2016) for an iterative method. In this paper, we establish fifth order of convergence of the method using assumptions only on the first Fréchet derivative of the involved operator. © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature.
Convergence of a Tikhonov Gradient Type-Method for Nonlinear Ill-Posed Equations
(Springer, 2017) George, S.; Shubha, V.S.; Padikkal, P.
In this study Tikhonov Gradient type-method is considered for nonlinear ill-posed operator equations. In our convergence analysis, we use hypotheses only on the first Frec?het derivative of F in contrast to the higher order Frec?het derivatives used in the earlier studies. We obtained ‘optimal’ order error estimate by choosing the regularization parameter according to the adaptive method proposed by Pereverzev and Schock (SIAM J Numer Anal 43(5):2060–2076, 2005). © 2017, Springer (India) Private Ltd.
Curvature driven diffusion coupled with shock for image enhancement/reconstruction
(Inderscience Publishers, 2011) Padikkal, P.; George, S.
Curvature driven diffusion is widely used for image denoising and inpainting. Among the curvature driven diffusion techniques Gauss Curvature Driven Diffusion (GCDD) became a prominent image denoising method due to its capability to retain some important structures with non zero curvatures, like curved edges, corners etc. Unlike many other non-linear diffusion techniques, the curvature driven diffusion hardly has any inverse diffusion characteristics. In this work we propose to introduce a shock term along with the GCDD term to enhance the edges while smoothing-out the noise. This technique will preserve some important structures and enhance them while denoising the image. The experiments clearly demonstrates the efficiency of the method. Copyright © 2011 Inderscience Enterprises Ltd.
Despeckling and enhancement of ultrasound images using non-local variational framework
(Springer Science and Business Media Deutschland GmbH, 2022) Febin, I.P.; Padikkal, P.
Speckles are introduced in the ultrasound data due to constructive and destructive interference of the probing signals that are used for capturing the characteristics of the tissue being imaged. There are a plethora of models discussed in the literature to improve the contrast and resolution of the ultrasound images by despeckling them. There is a class of models that assumes that the noise is multiplicative in its original form, and transforming the model to a log domain makes it an additive one. Nevertheless, such a transformation duly oversimplifies the scenario and does not capture the inherent properties of the data-correlated nature of speckles. Therefore, it results in poor reconstruction. This problem is addressed to a considerable extent in the subsequent works by adopting various models to address the data-correlated nature of the noise and its distributions. This work introduces a weberized non-local total bounded variational model based on the noise distribution built on the Retinex theory. This perceptually inspired model apparently restores and improves the contrast of the images without compromising much on the details inherently present in the data. The numerical implementation of the model is carried out using the Bregman formulation to improve the convergence rate and reduce the parameter sensitivity. The experimental results are highlighted and compared to demonstrate the efficiency of the model. © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature.
Despeckling of SAR Images Using Shrinkage of Two-Dimensional Discrete Orthonormal S-Transform
(World Scientific, 2021) Kamath, P.R.; Senapati, K.; Padikkal, P.
Speckles are inherent to SAR. They hide and undermine several relevant information contained in the SAR images. In this paper, a despeckling algorithm using the shrinkage of two-dimensional discrete orthonormal S-transform (2D-DOST) coefficients in the transform domain along with shock filter is proposed. Also, an attempt has been made as a post-processing step to preserve the edges and other details while removing the speckle. The proposed strategy involves decomposing the SAR image into low and high-frequency components and processing them separately. A shock filter is used to smooth out the small variations in low-frequency components, and the high-frequency components are treated with a shrinkage of 2D-DOST coefficients. The edges, for enhancement, are detected using a ratio-based edge detection algorithm. The proposed method is tested, verified, and compared with some well-known models on C-band and X-band SAR images. A detailed experimental analysis is illustrated. © 2021 World Scientific Publishing Company.