Browsing by Author "Senapati, K."

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A Novel Decision Level Class-Wise Ensemble Method in Deep Learning for Automatic Multi-Class Classification of HER2 Breast Cancer Hematoxylin-Eosin Images
(Institute of Electrical and Electronics Engineers Inc., 2024) Pateel, G.P.; Senapati, K.; Pandey, A.K.
The Human Epidermal Growth Factor Receptor 2 (HER2) is one of the aggressive subtypes of breast cancer. The HER2 status decides the requirement of breast cancer patients to receive HER2-targeted therapy. The HER2 testing involves combining Immunohistochemistry (IHC) screening, followed by fluorescence in situ hybridization (FISH) for cases where IHC results are equivocal. These tests may involve multiple trials, are time intensive, and tend to be more expensive for certain classes of people. Hematoxylin and Eosin (HE) staining is employed for visualizing general tissue morphology and is a routine, cost-effective method. In this study, we introduce a novel automated class-wise weighted average ensemble deep learning algorithm at the decision level. The proposed algorithm fuses three pre-trained deep-learning models at the decision level by assigning a weight to each class based on their performance of the model to classify the HE-stained breast histopathology images into multi-class HER2 statuses as HER2-0+, HER2-1+, HER2-2+, and HER2-3+. The class-wise weight allocation to the base classifiers is one of the key features of the proposed algorithm. The presented framework surpasses all the existing methods currently employed on the Breast Cancer Immunohistochemistry (BCI) dataset, establishing itself as a dependable approach for detecting HER2 status from HE-stained images. This study highlights the robustness of the proposed algorithm as well as the sufficient information encapsulated within HE-stained images for the effective detection of the HER2 protein present in breast cancer. Therefore, the proposed method possesses the potential to sideline the need for IHC laboratory tests, which hoard time and money. © 2013 IEEE.
CAEB7-UNet: An Attention-Based Deep Learning Framework for Automated Segmentation of C-Spine Vertebrae in CT Images
(Institute of Electrical and Electronics Engineers Inc., 2025) Pandey, A.K.; Senapati, K.; Pateel, G.P.
Accurate segmentation of vertebrae in computed tomography (CT) images possess serious challenges due to the irregular vertebral boundaries, low contrast and brightness, and noise in CT scans. This study presents a novel channel attention-based EfficientNetB7-UNet (CAEB7-UNet) method to address this complex task effectively. The proposed model introduces an upgraded ReLU-based channel attention module (CAM) in the skip connection which restrains the nonessential attributes by suppressing them and accentuates the relevant features by emphasizing them to boost the overall segmentation performance. In this work, an improved EfficientNetB7 is employed as the encoder for feature extraction, the fusion of local and global features is enhanced through the upgraded CAM in skip connection, and the up-sampling is performed in the decoder. Further, the model is optimized by incorporating hyperparameter optimization, specifically, hybrid learning rate scheduler strategies, along with the AdamW optimizer and custom data augmentation. A total of 34,782 CT images obtained from the RSNA-2022 cervical spine fracture detection challenge is utilized in this study. The proposed model achieves outstanding performance, yielding a dice score index (DSI) of 96.14% and mean intersection over union (mIoU) of 91.46%. Moreover, a comparative performance analysis of CAEB7-UNet with two state-of-the-art models is carried out on the same dataset. Our approach outperforms both the models, with the best one by 8.1%, 6.73%, 12.7%, and 11.98% in terms of DSI, mIoU, precision, and F1-score respectively. Additionally, it requires merely 0.38 seconds to generate the segmentation mask of a single slice of a CT scan. © 2013 IEEE.
Convergence analysis of a class of iterative methods: a unified approach
(Vilnius Gediminas Technical University, 2025) Murugan, M.; Godavarma, C.; George, S.; Bate, I.; Senapati, K.
In this paper, we study the convergence of a class of iterative methods for solving the system of nonlinear Banach space valued equations. We provide a unified local and semi-local convergence analysis for these methods. The convergence order of these methods are obtained using the conditions on the derivatives of the involved operator up to order 2 only. Further, we provide the number of iterations required to obtain the given accuracy of the solution. Various numerical examples including integral equations and Caputo fractional differential equations are considered to show the performance of our methods. © 2025 The Author(s). Published by Vilnius Gediminas Technical University.
Convergence Analysis of Jarratt-like Methods for Solving Nonlinear Equations for Thrice-Differentiable Operators
(Multidisciplinary Digital Publishing Institute (MDPI), 2025) Bate, I.; Senapati, K.; George, S.; Argyros, I.K.; Argyros, M.I.
The main goal of this paper is to study Jarratt-like iterative methods to obtain their order of convergence under weaker conditions. Generally, obtaining the (Formula presented.) -order convergence using the Taylor series expansion technique needed at least (Formula presented.) times differentiability of the involved operator. However, we obtain the fourth- and sixth-order for Jarratt-like methods using up to the third-order derivatives only. An upper bound for the asymptotic error constant (AEC) and a convergence ball are provided. The convergence analysis is developed in the more general setting of Banach spaces and relies on Lipschitz-type conditions, which are required to control the derivative. The results obtained are examined using numerical examples, and some dynamical system concepts are discussed for a better understanding of convergence ideas. © 2025 by the authors.
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.
Enhancing the applicability of Chebyshev-like method
(Academic Press Inc., 2024) George, S.; Bate, I.; M, M.; Godavarma, C.; Senapati, K.
Ezquerro and Hernandez (2009) studied a modified Chebyshev's method to solve a nonlinear equation approximately in the Banach space setting where the convergence analysis utilizes Taylor series expansion and hence requires the existence of at least fourth-order Fréchet derivative of the involved operator. No error estimate on the error distance was given in their work. In this paper, we obtained the convergence order and error estimate of the error distance without Taylor series expansion. We have made assumptions only on the involved operator and its first and second Fréchet derivative. So, we extend the applicability of the modified Chebyshev's method. Further, we compare the modified Chebyshev method's efficiency index and dynamics with other similar methods. Numerical examples validate the theoretical results. © 2024 Elsevier Inc.
Extended convergence for two-step methods with non-differentiable parts in Banach spaces
(Springer Science and Business Media B.V., 2024) Argyros, I.K.; George, S.; Senapati, K.
In this study, we have extended the applicability of two-step methods with non-differentiable parts for solving nonlinear equations defined in Banach spaces. The convergence analysis uses conditions weaker than the ones in earlier studies. Other advantages include computable a priori error distances based on generalized conditions, an extended region of convergence as well as a better knowledge of the isolation for the solutions. By setting the divided differences equal to zero the results can be used to solve equations with differentiable part too. © The Author(s), under exclusive licence to The Forum D’Analystes 2023.
Extended local convergence for Newton-type solver under weak conditions
(Babes-Bolyai University, 2021) Argyros, I.K.; George, S.; Senapati, K.
We present the local convergence of a Newton-type solver for equations involving Banach space valued operators. The eighth order of convergence wasshown earlier in the special case of the k-dimensional Euclidean space, usinghypotheses up to the eighth derivative although these derivatives do not appearin the method. We show convergence using only the first derivative. This way weextend the applicability of the methods. Numerical examples are used to showthe convergence conditions. Finally, the basins of attraction of the method, onsome test problems are presented © 2021, Studia Universitatis Babes-Bolyai Mathematica. All Rights Reserved.
Extending the applicability of the inexact Newton-HSS method for solving large systems of nonlinear equations
(Springer, 2020) Argyros, I.K.; George, S.; Senapati, K.
We revisit the study of the semi-local convergence of the inexact Newton-HSS method (INHSS) introduced by Amiri et al. (2018), for solving large systems of nonlinear equations. In particular, first we present the correct convergence criterion, since the one in the preceding reference is incorrect. Secondly, we present an even weaker convergence criterion using our idea of recurrent functions. Moreover, the bound functions are compared. Finally, numerical examples are provided to show that the earlier convergence criteria are not satisfied but the new ones are satisfied. Hence, the applicability of the INHSS method is extended and under the same information as in the earlier studies. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.
Improving the performance of multi-stage HER2 breast cancer detection in hematoxylin-eosin images based on ensemble deep learning
(Elsevier Ltd, 2025) Pateel, G.P.; Senapati, K.; Pandey, A.K.
Background: Breast cancer is the most frequently diagnosed cancer among women worldwide, and histopathology is the gold standard in diagnosing the disease. Hematoxylin and Eosin (HE) staining, routinely employed to observe the overall tissue structure, is an affordable and commonly practiced cancer diagnosis. In contrast, Immunohistochemistry (IHC), which detects the increased presence of particular antigens linked to the mutation, can require multiple tests to conduct and is relatively costly. Generally, in computer-aided diagnosis, the conventional methods rely on a single network to extract features. However, these methods have significant limitations and fail to generalize. Methods: In this study, we propose an automated novel weighted average algorithm called HER2-ETNET, which ensembles the chosen three pre-trained deep learning models, DenseNet 201, GoogLeNet, and ResNet-50, to classify breast histopathology HE images into multi-class Human Epidermal Growth Factor Receptor-2 (HER2) status (HER2-0+, HER2-1+, HER2-2+, HER2-3+). The proposed method has the potential to bypass the IHC laboratory test. In this study, we form a weight matrix by fusing together, the scores of False Positive Rate (FPR) and False Negative Rate (FNR) of both training and validation sets, and the computed weights are assigned to the three base learners. This is in contrast to the previous works, in which the weights were generally assigned empirically to the chosen deep learning models, which might be erroneous. Result: The proposed approach is evaluated on the unseen test set, and it achieves accuracy, precision, recall and AUC of 97.44%, 97.32%, 97.39%, and 99.75% respectively. Conclusion: The proposed framework outperforms all the existing methods on the same dataset and is proven to be the reliable method in detecting the HER2 status (HER2-0+, HER2-1+, HER2-2+, HER2-3+) from HE images. This also proves that, HE stained images contain adequate information for efficiently detecting the HER2 status in breast cancer. © 2024 Elsevier Ltd
Improving Vertebral Fracture Detection in C-Spine CT Images Using Bayesian Probability-Based Ensemble Learning
(Multidisciplinary Digital Publishing Institute (MDPI), 2025) Pandey, A.K.; Senapati, K.; Argyros, I.K.; Pateel, G.P.
Vertebral fracture (VF) may induce spinal cord injury that can lead to serious consequences which eventually may paralyze the entire or some parts of the body depending on the location and severity of the injury. Diagnosis of VFs is crucial at the initial stage, which may be challenging because of the subtle features, noise, and homogeneity present in the computed tomography (CT) images. In this study, Wide ResNet-40, DenseNet-121, and EfficientNet-B7 are chosen, fine-tuned, and used as base models, and a Bayesian-based probabilistic ensemble learning method is proposed for fracture detection in cervical spine CT images. The proposed method considers the prediction’s uncertainty of the base models and combines the predictions obtained from them, to improve the overall performance significantly. This method assigns weights to the base learners, based on their performance and confidence about the prediction. To increase the robustness of the proposed model, custom data augmentation techniques are performed in the preprocessing step. This work utilizes 15,123 CT images from the RSNA-2022 C-spine fracture detection challenge and demonstrates superior performance compared to the individual base learners, and the other existing conventional ensemble methods. The proposed model also outperforms the best state-of-the-art (SOTA) model by 1.62%, 0.51%, and 1.29% in terms of accuracy, specificity, and sensitivity, respectively; furthermore, the AUC score of the best SOTA model is lagging by 5%. The overall accuracy, specificity, sensitivity, and F1-score of the proposed model are 94.62%, 93.51%, 95.29%, and 93.16%, respectively. © 2025 by the authors.
Iteration of certain exponential-like meromorphic functions
(Springer, 2018) Chakra, T.K.; Nayak, T.; Senapati, K.
The dynamics of functions f?(z)=?ezz+1forz?C,?>0 is studied showing that there exists ??> 0 such that the Julia set of f? is disconnected for 0 < ?< ?? whereas it is the whole Riemann sphere for ?> ??. Further, for 0 < ?< ??, the Julia set is a disjoint union of two topologically and dynamically distinct completely invariant subsets, one of which is totally disconnected. The union of the escaping set and the backward orbit of ? is shown to be disconnected for 0 < ?< ?? whereas it is connected for ?> ??. For complex ?, it is proved that either all multiply connected Fatou components ultimately land on an attracting or parabolic domain containing the omitted value of the function or the Julia set is connected. In the latter case, the Fatou set can be empty or consists of Siegel disks. All these possibilities are shown to occur for suitable parameters. Meromorphic functions En(z)=ez(1+z+z22!+?+znn!)-1, which we call exponential-like, are studied as a generalization of f(z)=ezz+1 which is nothing but E1(z). This name is justified by showing that En has an omitted value 0 and there are no other finite singular value. In fact, it is shown that there is only one singularity over 0 as well as over ? and both are direct. Non-existence of Herman rings are proved for ?En. © 2018, Indian Academy of Sciences.
Jarratt-type methods and their convergence analysis without using Taylor expansion
(Elsevier Inc., 2025) Bate, I.; Senapati, K.; George, S.; M, M.; Godavarma, C.
In this paper, we study the local convergence analysis of the Jarratt-type iterative methods for solving non-linear equations in the Banach space setting without using the Taylor expansion. Convergence analysis using Taylor series required the operator to be differentiable at least p+1 times, where p is the order of convergence. In our convergence analysis, we do not use the Taylor expansion, so we require only assumptions on the derivatives of the involved operator of order up to three only. Thus, we extended the applicability of the methods under study. Further, we obtained a six-order Jarratt-type method by utilising the method studied by Hueso et al. in 2015. Numerical examples and dynamics of the methods are presented to illustrate the theoretical results. © 2024 Elsevier Inc.
Local convergence analysis of two iterative methods
(Springer Science and Business Media B.V., 2022) George, S.; Argyros, I.K.; Senapati, K.; Kanagaraj, K.
In this paper we consider two three-step iterative methods with common first two steps. The convergence order five and six, respectively of these methods are proved using assumptions on the first derivative of the operator involved. We also provide dynamics of these methods © 2022, The Author(s), under exclusive licence to The Forum D’Analystes.
On obtaining convergence order of a fourth and sixth order method of Hueso et al. without using Taylor series expansion
(Elsevier B.V., 2024) M, M.; Godavarma, G.; George, S.; Bate, I.; Senapati, K.
Hueso et al. (2015) studied the fourth and sixth order methods to approximate a solution of a nonlinear equation in Rn, where the convergence analysis needs the involved operator to be five times differentiable and seven times differentiable for fourth-order and sixth-order methods, respectively. Also, they found no error estimate for those methods, as the Taylor series expansion played a leading role in proving the convergence. In this paper, we extended the method in the Banach space settings and relaxed the higher order derivative of the involved operator so that the methods can be used in a bigger class of problems which were not covered by the analysis in Hueso et al. (2015). Also, we obtained an error estimate without Taylor series expansion. This error estimate helps to get the number of iterations to achieve a given accuracy. Moreover, new sixth-order method is introduced by small modification and numerical examples were discussed for all these methods to validate our theoretical results and to study the dynamics. © 2024 Elsevier B.V.
Short-term wind speed forecasting using S-transform with compactly supported kernel
(John Wiley and Sons Ltd, 2021) Kamath, P.R.; Senapati, K.
This paper presents a modified S-transform (ST) based on a compactly supported kernel. A version of Cheriet-Belochrani (CB) kernel is chosen for this purpose. It is shown that the proposed modified S-transform (CBST) offers better frequency resolution than the traditional ST. It is used to decompose the wind speed time series into frequency-based subseries. Further, artificial neural network (ANN) is applied to each of the subseries for an hour ahead prediction. Finally, forecast for the original wind speed series is obtained by combining the prediction result of all the subseries. Initially, increasing the number of subseries results in a decrease in prediction error. However, when the number of subseries is sufficiently large, no significant change in prediction error is observed if the number is further increased. It is also observed that, for a model based on neural-network, involving decomposition of wind speed time series, the proposed model offers low prediction error. A comparative study with the methods based on wavelet transform (WT) and empirical mode decomposition (EMD) demonstrates the effectiveness of the proposed method. For this study, we have used simulated wind speed data generated by nonhydrostatic mesoscale model and data recorded using anemometer and LiDAR instrument at different heights to evaluate the short-term forecasting results. © 2020 The Authors. Wind Energy published by John Wiley & Sons Ltd
Shrinking generators based on ?-LFSRs
(Elsevier B.V., 2020) Bishoi, S.K.; Senapati, K.; Shankar, B.R.
The word-based LFSRs called ?-LFSRs are very attractive as they take advantage of the modern word-based processor and thus increase the throughput. Secondly, the bitstream produced by ?-LFSR has excellent statistical properties with a high period except for low linear complexity. In order to increase the linear complexity, the concept of both bit-oriented shrinking and self-shrinking generators is introduced in case of ?-LFSRs. In both the cases, the lower bound for the period as well as for the linear complexity of the bitstream are shown to be exponential. Further, we have experimented and investigated more results on the periodicity and statistical properties of the bitstream in self-shrinking ?-LFSRs. This helps to find and prove the exact period of the bitstream produced by self-shrinking generators. © 2020 Elsevier B.V.
Timeâ€“Frequencyâ€“Phase analysis for automatic detection of ocular artifact in EEG signal using S-transform
(Springer Verlag service@springer.de, 2019) Senapati, K.; Kamath, P.R.
Artifacts are unwanted components in the EEG signals which may affect the EEG signal reading, thereby not allowing the signal to be interpreted properly. One of the most common artifacts is the ocular artifact. This artifact arises due to the movement of the eye including eye blink. In most cases, detection of ocular artifacts in EEG signals is done by skilled professionals who are small in number. This paper proposes a new approach of automatic detection of ocular artifacts using the phase information present in the S-transform (ST) of EEG signal. S-transform of a signal provides absolutely referenced phase information of the signal in addition to timeâ€“frequency information. A time delay exists between the signals recorded by electrodes placed at different distances from the point of origin of the artifact. This time delay translates to phase delay in the frequency domain. The phase information of the EEG signal recorded from different electrodes placed in the frontal region is used to detect the artifacts which are generated near the region where the eye is located. Â© Springer Nature Singapore Pte Ltd 2019.
Time�Frequency�Phase analysis for automatic detection of ocular artifact in EEG signal using S-transform
(2019) Senapati, K.; Kamath, P.R.
Artifacts are unwanted components in the EEG signals which may affect the EEG signal reading, thereby not allowing the signal to be interpreted properly. One of the most common artifacts is the ocular artifact. This artifact arises due to the movement of the eye including eye blink. In most cases, detection of ocular artifacts in EEG signals is done by skilled professionals who are small in number. This paper proposes a new approach of automatic detection of ocular artifacts using the phase information present in the S-transform (ST) of EEG signal. S-transform of a signal provides absolutely referenced phase information of the signal in addition to time�frequency information. A time delay exists between the signals recorded by electrodes placed at different distances from the point of origin of the artifact. This time delay translates to phase delay in the frequency domain. The phase information of the EEG signal recorded from different electrodes placed in the frontal region is used to detect the artifacts which are generated near the region where the eye is located. � Springer Nature Singapore Pte Ltd 2019.