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1

Performance evaluation of optimized deep learningmodel with Multilayered Max-Norm Regularization (MMNR) technique for brain tumour classificationin MRI multi-modal images

Binish Mulackal Chandran, Thomas Vinu

Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska

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2026

|

T. 16, nr 2

5--14

EN

Brain tumours are aggressive malignant diseases, both in children and adults, representing 86 to 92 percent of all primary and almost half of secondary Central Nervous System (CNS) tumours. For individuals with malignant brain or central nervous system (CNS) tumours, the 5-year survival rate is about 34% for males and 36% for women. Brain tumours can be classified into several types, including benign, malignant, pituitary, etc. This study proposes a new architecture named Multilayered Max-Norm Regularization CNN (MMNR-CNN) and investigates the performance of this model for the classification of brain tumours in multi-modal MRI images. The model incorporates Markov Random Field (MRF) for bias field correction, and Monte Carlo Dropout to quantify prediction uncertainty through stochastic forward passes, enhancing the model's reliability in clinical decisionmaking. Furthermore, we integrate Explainable AI (XAI) techniques using Gradient-weighted Class Activation Mapping (Grad-CAM) to visually interpret the regions of MRI scans that contribute most to the classification decisions. We present a complete analysis of the Multilayered Max-Norm Regularization model trained on augmented brain image data and compare the performance on different values of regularization parameters that lead to the automatic selection of spatially important features for the classification task. This increases the generalization and robustness of the training dataset through augmentation. The model is trained using the Br35H database and the Figshare database. Both are used primarily for research in brain tumour detection and classification. The obtained performance metrics are the best in the literature, with a testing accuracy of 99.88% and 100 % precision.

PL

Guzy mózgu to agresywne choroby złośliwe, zarówno u dzieci, jak i u dorosłych, stanowiące 86–92% wszystkich pierwotnych i prawie połowę wtórnych guzów ośrodkowego układu nerwowego (OUN). U osób ze złośliwymi guzami mózgu lub ośrodkowego układu nerwowego (OUN) 5-letni wskaźnik przeżycia wynosi około 34% dla mężczyzn i 36% dla kobiet. Guzy mózgu można podzielić na kilka typów, w tym łagodne, złośliwe, przysadkowe itp. W niniejszym badaniu zaproponowano nową architekturę o nazwie Wielowarstwową Techniką Ograniczenia Normy Maksymalnej (Multilayered MaxNorm Regularization CNN – MMNR-CNN) i zbadano wydajność tego modelu w klasyfikacji guzów mózgu w wielomodalnych obrazach MRI. Model wykorzystuje losowe pole Markowa (MRF) do korekcji pola błędu oraz metodę Monte Carlo Dropout do ilościowego określania niepewności prognozy poprzez stochastyczne przejścia do przodu, zwiększając niezawodność modelu w podejmowaniu decyzji klinicznych. Ponadto integrujemy techniki XAI (Exploreable AI) wykorzystujące Gradient-weighted Class Activation Mapping (Grad-CAM), aby wizualnie zinterpretować obszary skanów MRI, które mają największy wpływ na decyzje klasyfikacyjne. Przedstawiamy pełną analizę modelu MMNR wytrenowanego na rozszerzonych danych obrazowych mózgu i porównujemy wydajność przy różnych wartościach parametrów regularyzacji, które prowadzą do automatycznego wyboru cech istotnych przestrzennie dla zadania klasyfikacji. Zwiększa to generalizację i odporność zbioru danych treningowych poprzez rozbudowę. Model jest trenowany z wykorzystaniem bazy danych Br35H i Figshare. Obie są wykorzystywane głównie w badaniach nad wykrywaniem i klasyfikacją guzów mózgu. Uzyskane wskaźniki wydajności są najlepsze w literaturze, z dokładnością testowania na poziomie 99,88% i 100% precyzją.

2

Elastic least-squares reverse time migration with curvelet-domain and structural tensor regularization

Wang Mingqian, He Bingshou, Lin Yuzhao

Acta Geophysica

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2026

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vol. 74, no. 3

art. no. 141, s. 1--16

EN

Elastic least-squares reverse time migration improves the resolution and amplitude fidelity of multicomponent seismic imaging through iterative inversion of reflectivity models. However, conventional elastic least-squares reverse time migration still suffers from noise, artifacts, and instability due to the ill-posed nature of the inverse problem, especially in geologically complex settings. To address these challenges, a novel elastic least-squares reverse time migration method is proposed, incorporating structure tensor-guided total variation regularization and curvelet-domain sparsity constraints. The structure tensor extracts locally dominant orientations from image gradients. When combined with total variation regularization, it enables edge-preserving smoothing and enhances structural continuity while suppressing artifacts across structural boundaries. In addition, the curvelet transform provides a multiscale and multidirectional sparse representation of the reflectivity image, and the curvelet-domain constraint effectively reduces migration noise and artifacts. This hybrid regularization strategy restricts model updates to subspaces that are both structurally consistent and sparsely represented. Numerical experiments on a synthetic graben model and the SEG/EAGE overthrust model indicate that, compared with conventional methods, the proposed method effectively suppresses noise and artifacts, producing images with improved structural consistency and lower model error.

3

A mixed-order minimum entropy regularization for inversion of magnetic data

Rezaie Mohammad

Acta Geophysica

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2026

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vol. 74, no. 3

art. no. 170, s. 1--16

EN

The inversion of magnetic data is a crucial geophysical technique for imaging subsurface structures, but it is inherently nonunique. Regularization is essential to obtain geologically plausible solutions, with stabilizers based on L2 norms often producing overly smooth models that obscure boundaries, while sparse constraints can lead to artificially concentrated features with exaggerated susceptibilities. This paper introduces a novel framework for magnetic data inversion utilizing a mixed-order minimum entropy stabilizer, which integrates both first- and second-order probability measures within a pseudo-quadratic form. The proposed method is designed to mitigate the limitations of its individual components, striking a balance between the excessive focusing of first-order minimum entropy and the over-smoothing of second-order minimum entropy stabilizers. To achieve the solution, we use a reweighted regularized conjugate gradient (RRCG) algorithm as an efficient approach. The efficacy of this approach is demonstrated through comprehensive testing on two synthetic models—a dipping dike and two cuboids—and a field dataset from the Nikka volcanogenic massive sulfide (VMS) deposit in Ontario. Results show that the mixed-order stabilizer consistently generates compact models with clearly defined boundaries and accurate susceptibility values, outperforming the conventional methods. This study confirms that the mixed-order minimum entropy regularization provides a robust and effective tool for producing geologically realistic subsurface models from magnetic data, enhancing interpretation accuracy in exploration geophysics.

4

A modified Distributed Scatterer InSAR method: A case study on potential landslide body detection in Faer Town, China

Nie Zhibo, Ding Mintao, Ding Shijun, Wang Xvli, Jiang Keru, Zhang Jinfeng

Reports on Geodesy and Geoinformatics

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2025

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Vol. 119

99--108

EN

Landslides near critical infrastructure, such as power transmission lines, represent significant safety and economic risks, especially in regions prone to geohazards. Early detection and monitoring are essential to mitigate potential damage. Interferometric Synthetic Aperture Radar (InSAR) technology has become a powerful tool for detecting slow-moving landslides and monitoring millimetre-scale ground displacements over time. Among the various satellite data sources, Sentinel-1 provides consistent and high-resolution data, advancing research in landslide kinematics and instability prediction. However, accurate delineation of landslide-affected areas remains particularly challenging in densely vegetated regions, where signal decorrelation limits traditional methods. To address these limitations, this study introduces a modified Distributed Scatterer InSAR (DSI) method designed to assess landslide velocity more effectively. The proposed approach incorporates a regularization technique into the covariance matrix estimation process, reducing phase estimation bias and improving the signal-to-noise ratio of displacement time series. The modified DSI method was applied to the Faer Town landslide in Guizhou Province, Southwest China. Results from synthetic and real-data experiments demonstrate significant improvements in the accuracy and reliability of landslide velocity detection, with a higher density of reliable measurement points compared to traditional approaches. These findings highlight the method's potential for enhancing landslide monitoring and risk mitigation in challenging environments.

5

Identyfikacja niestacjonarnych kanałów komunikacyjnych

Ciołek Marcin

Przegląd Telekomunikacyjny + Wiadomości Telekomunikacyjne

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2025

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nr 4

82--85

PL

W niniejszym artykule rozważany jest problem identyfikacji niestacjonarnych kanałów komunikacyjnych o rzadkiej strukturze, z użyciem lokalnych funkcji bazowych. Typowe algorytmy wykorzystują regularyzację ℓ1, która nie zawsze ma rozwiązanie analityczne i wymaga wtedy kosztownego wyszukiwania numerycznego. Proponowany jest szybki regularyzowany lokalny estymator funkcji bazowych, oparty na przybliżonej regularyzacji ℓ2.

EN

In this paper identification of nonstationary communication channels with sparse structure using local basis functions is addressed. While standard approaches rely on ℓ1 regularization, in cases where no closed-form solution exists, they require a computationally expensive numerical search. A fast regularized local basis functions algorithm based on reweighted ℓ2 regularization is proposed.

6

Finding the sweet spot: a study of data augmentation intensity for small-scale image classification

Swastika Windra

Journal of Automation Mobile Robotics and Intelligent Systems

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2025

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Vol. 19, No. 4

94--101

EN

Finding the optimal level of data augmentation intensity remains one of the most challenging aspects of training deep learning models on small-scale datasets, which is particularly relevant for resource-constrained environments in robotics and automation systems. While data augmentation is universally recognized as essential for preventing overfitting and improving generalization, excessive augmentation can paradoxically harm model performance by introducing too much variability in the training data. This research investigates the “sweet spot” of augmentation intensity through a comprehensive study of six distinct augmentation strategies on CIFAR-10, a representative small-scale image classification benchmark commonly used in mobile robotics applications. We designed a controlled experiment comparing: No Augmentation (baseline), Basic torchvision transforms, Light Advanced albumentations, Moderate Advanced geometric-photometric combinations, Strong Advanced with noise injection, and AutoAugment Style with complex transformations. Our findings reveal a clear relationship between augmentation intensity and model performance, with peak performance achieved at moderate intensity levels (Basic strategy with intensity score [IS] 0.49). The Basic augmentation strategy achieved 79.84% validation accuracy, significantly outperforming both minimal augmentation (77.49%) and excessive augmentation (71.64%). Through statistical analysis including correlation studies (Pearson 𝑟 = −0.759, 𝑝 = 0.080; Spearman 𝜌 = −0.714, 𝑝 = 0.111), the “sweet spot” lies in balanced augmentation that provides regularization benefits without overwhelming the learning proces.

7

Regularization for electricity price forecasting

Uniejewski Bartosz

Operations Research and Decisions

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2024

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Vol. 34, No. 3

267--286

EN

The most commonly used form of regularization typically involves defining the penalty function as a ℓ 1or ℓ2 norm. However, numerous alternative approaches remain untested in practical applications. In this study, we apply ten different penalty functions to predict electricity prices and evaluate their performance under two different model structures and in two distinct electricity markets. The study reveals that LQ and elastic net consistently produce more accurate forecasts compared to other regularization types. In particular, they were the only types of penalty functions that consistently produced more accurate forecasts than the most commonly used LASSO. Furthermore, the results suggest that cross-validation outperforms Bayesian information criteria for parameter optimization, and performs as well as models with ex-post parameter selection.

8

Global in time well-posedness of a three-dimensional periodic regularized Boussinesq system

Almutairi Shahah

Demonstratio Mathematica

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2024

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Vol. 57, nr 1

art. no. 20240002

EN

Global in time weak solution to a regularized periodic three-dimensional Boussinesq system is proved to exist in energy spaces. This solution depends continuously on the initial data. In particular, it is unique. The main novelty is the global in time aspect of this solution. The proofs use the coupling between the temperature and the velocity of the fluid, energy methods, and compactness argument.

9

On some inverse problem for bi-parabolic equation with observed data in Lp spaces

Tuan Nguyen Huy

Opuscula Mathematica

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2022

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Vol. 42, no. 2

305--335

EN

The bi-parabolic equation has many practical significance in the field of heat transfer. The objective of the paper is to provide a regularized problem for bi-parabolic equation when the observed data are obtained in Lp. We are interested in looking at three types of inverse problems. Regularization results in the L2 space appears in many related papers, but the survey results are rare in Lp, p ̸= 2. The first problem related to the inverse source problem when the source function has split form. For this problem, we introduce the error between the Fourier regularized solution and the exact solution in Lp spaces. For the inverse initial problem for both linear and nonlinear cases, we applied the Fourier series truncation method. Under the terminal input data observed in Lp, we obtain the approximated solution also in the space Lp. Under some reasonable smoothness assumptions of the exact solution, the error between the the regularized solution and the exact solution are derived in the space Lp. This paper seems to generalize to previous results for bi-parabolic equation on this direction.

10

Two-step inversion of airborne geophysical data: a stable downward continuation approach for physical modelling

Azadi Majid, Abedi Maysam, Norouzi Gholam-Hossain

Acta Geophysica

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2022

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Vol. 70, no 1

121--139

EN

Airborne potential field geophysical survey is employed for a variety of purposes to cover in a cost-effective manner large prospect areas. Despite the many advantages of airborne data measurements, due to the height from the ground, the received response is weakened (signal attenuation) and causes inadequacies in data representation. Accordingly, it is expected that the inversion results are far from reality and there are shortcomings in the retrieved model. This study investigates the impact of airborne survey on small-sized magmatic units, where directly inverting airborne data suffer from signal attenuation and lead to the loss of the causative model. In this study we improved the airborne data inversion by mixing a two-step cooperative approach which enhances the potential field data by a stable downward continuation to the ground surface in the spectral domain, and subsequently running a physical property modelling. The efficiency of the method over one-step airborne data inversion is examined for a synthetic multi-source case (magnetic and gravity) and then is used to find out the close spatial link between magnetometry signatures and iron–phosphate sources in the Esfordi district in Iran. The results showed that the proposed method performed better than direct inversion of airborne data and could satisfactorily identify the sources of the anomaly.

11

Determinig of the sound power of the fan in in situ conditions using the virtual reference source method

Suder-Dębska Katarzyna, Czajka Ireneusz, Łojek Paweł

Vibrations in Physical Systems

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2021

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Vol. 32, nr 2

art. no. 2021206

EN

Sound power is one of the basic parameters characterizing the sound source and has a direct impact on the acoustic climate in its surroundings. Therefore, the determining of the sound power of machines is a practical problem. While there are many methods of determining the sound power, each of them has its own limitations. The authors presented the implementation of a comparative method of determining the sound power with the use of a virtual reference source. The method was used to test a high-efficiency flue gas exhaust fan installed on a laboratory stand. The sound source was placed in the geometric centre of the fan and the acoustic field distribution in the room was determined using geometrical methods. After determining the influence factors, the value of the source sound power of the source was calculated by means of the Moore-Penrose pseudo-inverse. Since the problem under study belongs to the inverse problems, the Tikhonov regularization was used, where the value of the parameter α was determined by the L-curve method.

12

Regularization based discriminative feature pattern selection for the classification of Parkinson cases using machine learning

Kaliyan Kamalakannan, Ganesan Anandharaj

Bio-Algorithms and Med-Systems

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2021

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Vol. 17, no. 3

181--189

EN

Objectives: This paper focuses on developing a regularization-based feature selection approach to select the most effective attributes from the Parkinson’s speech dataset. Parkinson’s disease is a medical condition that progresses as the dopamine-producing nerve cells are affected. Early diagnosis often reduces the effect on the individuals, minimizes the advancement over time. In recent times, intelligent computational models are used in many complex cases to diagnose a clinical condition with high precision. These models are intended to find meaningful representation from the data to diagnose the disease. Machine learning acts as a tool, gears up the model learning process through a mathematical baseline. But, not in all cases, machine learning will be demanded to perform optimally. It comes with a few constraints, mainly the representation of the data. The learning models expect a clean, noise-free input, which in-turns produces better discriminative patterns over different categories of classes. Methods: The proposed model identified five candidate features as predictors. This feature subset is trained with different varieties of supervised classifiers to trace out the best-performing model. Results: The results are validated through accuracy, precision, recall, and receiver’s operational characteristic curves. The proposed regularization- based feature selection model outperformed the benchmark algorithms by attaining 100% accuracy on most of the classifiers, other than linear discriminant analysis (99.90%) and naïve Bayes (99.51%). Conclusions: This paper exhibits the need for intelligent models to analyze complex data patterns to assist medical practitioners in better disease diagnosis. The results exhibit that the regularization methods find the best features based on their importance score, which improved the model performance over other feature selection methods.

13

An inverse backward problem for degenerate two-dimensional parabolic equation

Atifi Khalid, Essoufi El-Hassan, Khouiti Bouchra

Opuscula Mathematica

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2020

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Vol. 40, no. 4

427--449

EN

This paper deals with the determination of an initial condition in the degenerate two-dimensional parabolic equation [formula], where Ω is an open, bounded subset of R2, a [formula] with a ≥0 everywhere, and [formula], with initial and boundary conditions [formula] from final observations. This inverse problem is formulated as a minimization problem using the output least squares approach with the Tikhonov regularization. To show the convergence of the descent method, we prove the Lipschitz continuity of the gradient of the Tikhonov functional. Also we present some numerical experiments to show the performance and stability of the proposed approach.

14

A Phase Field Approach to Limited-angle Tomographic Reconstruction

Turpin Léonard, Roux Stéphane, Caty Olivier, Denneulin Sébastien

Fundamenta Informaticae

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2020

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Vol. 172, nr 2

203--219

EN

The tomography of an object with limited angle can be addressed through Iterative Reconstruction Reprojection (IRR) procedure, where in a standard reconstruction procedure is used together with a "filtering" of the image at each iteration. It is here proposed to use as a filter a phase-field — or Cahn-Hilliard — regularization interlaced with a filtered back-projection reconstruction. This reconstruction procedure is tested on a cone-beam tomography of a 3D woven ceramic composite material, and is shown to retrieve a reconstructed volume with very low artifacts in spite of a large missing angle interval (up to 28%).

15

Simulations of concrete response to impact loading using two regularized models

Wosatko Adam, Winnicki Andrzej, Pamin Jerzy

Computer Assisted Methods in Engineering and Science

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2020

|

Vol. 27, no. 1

27--60

EN

This paper focuses on a comparison of two regularized continuum models for concrete in the simulations of selected benchmarks of response to impact loading. Their overview is performed in the context of application in dynamics. The first one is the Hoffman viscoplastic consistency model, where the strain rate activates regularization. The second model is derived from the scalar damage theory enhanced by an averaging equation incorporating the Laplacian of an averaged strain measure. Both models are implemented in the FEAP package. The results of some standard wave propagation tests are discussed, considering discretization sensitivity and predicted failure modes. Three examples are pre- sented: the direct tension of a plain and reinforced concrete bar, the split test of a cylinder, and the four-point bending of a reinforced concrete beam. The ability of both models to simulate impact loading is assessed.

16

The regularization method in the classification task according to given examples

Kwiatkowski Włodzimierz

Przegląd Teleinformatyczny

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2019

|

T. 7, Nr 3-4 (49)

3--13

EN

The article considers the problem of classification based on the given examples of classes. As a feature vector, a complete characteristic of object is assumed. The peculiarity of the problem being solved is that the number of examples of the class may be less than the dimension of the feature vector, and also most of the coordinates of the feature vector can be correlated. As a consequence, the feature covariance matrix calculated for the cluster of examples may be singular or ill-conditioned. This disenable a direct use of metrics based on this covariance matrix. The article presents a regularization method involving the additional use of statistical properties of the environment.

PL

W artykule rozpatrywany jest problem klasyfikacji na podstawie wskazanych przykładów klas. Jako wektor cech przyjmuje się kompletną charakterystykę obiektów. Osobliwość rozwiązywanego zadania wynika z tego, że liczba przykładów klasy może być mniejsza od wymiaru wektora cech, a także wektor cech może zawierać współrzędne skorelowane. W konsekwencji macierz kowariancji cech obliczana dla klastra przykładów może być osobliwa albo źle uwarunkowana. Uniemożliwia to bezpośrednie stosowanie metryk bazujących na tej macierzy kowariancji. W artykule została przedstawiona metoda regularyzacji polegająca na dodatkowym wykorzystaniu statystycznych właściwości środowiska.

17

Implications of Pooling Strategies in Convolutional Neural Networks: A Deep Insight

Sharma Shallu, Mehra Rejesh

Foundations of Computing and Decision Sciences

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2019

|

Vol. 44, No. 3

303--330

EN

Convolutional neural networks (CNN) is a contemporary technique for computer vision applications, where pooling implies as an integral part of the deep CNN. Besides, pooling provides the ability to learn invariant features and also acts as a regularizer to further reduce the problem of overfitting. Additionally, the pooling techniques significantly reduce the computational cost and training time of networks which are equally important to consider. Here, the performances of pooling strategies on different datasets are analyzed and discussed qualitatively. This study presents a detailed review of the conventional and the latest strategies which would help in appraising the readers with the upsides and downsides of each strategy. Also, we have identified four fundamental factors namely network architecture, activation function, overlapping and regularization approaches which immensely affect the performance of pooling operations. It is believed that this work would help in extending the scope of understanding the significance of CNN along with pooling regimes for solving computer vision problems.

18

On regularization properties of artificial datasets for deep learning

Antczak Karol

Computer Science and Mathematical Modelling

|

2019

|

No. 9

13--18

EN

The paper discusses regularization properties of artificial data for deep learning. Artificial datasets allow to train neural networks in the case of a real data shortage. It is demonstrated that the artificial data generation process, described as injecting noise to high-level features, bears several similarities to existing regularization methods for deep neural networks. One can treat this property of artificial data as a kind of “deep” regularization. It is thus possible to regularize hidden layers of the network by generating the training data in a certain way.

PL

W artykule omówiono własności regularyzacyjne sztucznych danych używanych w uczeniu głębokim. Dane te pozwalają na uczenie sieci neuronowych w sytuacji niedoboru danych rzeczywistych. Okazuje się, że proces generacji danych sztucznych, opisany jako zaszumianie wysokopoziomowych cech, wykazuje wiele podobieństw do istniejących metod regularyzacyjnych dla głębokich sieci neuronowych. Dzięki temu możliwa jest regularyzacja warstw ukrytych sieci poprzez generowanie sztucznych danych uczących w odpowiedni sposób.

19

Reflected wave least squares reverse time migration with angle illumination compensation

Zhou Huamin, Chen Shengchang, Zhou Liming, Ren Haoran, Wu Rushan, Xiao Guoqiang

Acta Geophysica

|

2019

|

Vol. 67, no. 6

1551--1561

EN

High-quality seismic data imaging plays an important role in the lithological interpretation of subsurface structures. However, high-quality imaging remains a challenging task. Based on the linear inversion theory of reflected wave equations, this paper proposes reflected wave least squares reverse time migration with angle illumination compensation to better balance the amplitude of seismic imaging. We use the reflected wave migration equation to unify forward and backward propagation, which helps to obtain an image with correct phase and symmetric waveform. Under the assumption that the spectrum of seismic wavefield remains unchanged, the Poynting vector method is used to efficiently calculate the propagation direction of seismic waveform and seismic illumination in the angle domain. During iteration, angle-domain illumination is used as a preconditioner to compensate for the amplitude of the iterated gradient terms based on the angle value. In this manner, we can enhance the imaging energy of steeply inclined structures. To improve the stability of linear inversion, the spatial derivative of the image is used as a regularized constraint term. Numerical tests show that the proposed method can suppress imaging noise as well as improve resolution and amplitude fidelity of the images. Furthermore, the inversed result can be used to estimate underground reflectivity, which is important for the further development of seismic inversion technology.

20

Multichannel antileakage least squares spectral analysis for seismic data regularization beyond aliasing

Ghaderpour Ebrahim

Acta Geophysica

|

2019

|

Vol. 67, no. 5

1349--1363

EN

The antileakage least-squares spectral analysis is a new method of regularizing irregularly spaced data series. This method mitigates the spectral leakages in the least-squares spectrum caused by non-orthogonality of the sinusoidal basis functions on irregularly spaced series, and it is robust when data series are wide-sense stationary. An appropriate windowing technique can be applied to adapt this method to non-stationary data series. When data series present mild aliasing, this method can efectively regularize the data series; however, additional information or assumption is needed when the data series is coarsely sampled. In this paper, we show how to incorporate the spatial gradients of the data series into the method to regularize data series presenting severe aliasing and show its robust performance on synthetic and marine seismic data examples.