Selected work

Representative Papers

Matching of SAR and optical images based on transformation to shared modality

Feb 13, 2026

Significant differences in optical images and Synthetic Aperture Radar (SAR) images are caused by fundamental differences in the physical principles underlying their acquisition by Earth remote sensing platforms. These differences make precise image matching (co-registration) of these two types of images difficult. In this paper, we propose a new approach to image matching of optical and SAR images, which is based on transforming the images to a new modality. The new image modality is common to both optical and SAR images and satisfies the following conditions. First, the transformed images must have an equal pre-defined number of channels. Second, the transformed and co-registered images must be as similar as possible. Third, the transformed images must be non-degenerate, meaning they must preserve the significant features of the original images. To further match images transformed to this shared modality, we train the RoMa image matching model, which is one of the leading solutions for matching of regular digital photographs. We evaluated the proposed approach on the publicly available MultiSenGE dataset containing both optical and SAR images. We demonstrated its superiority over alternative approaches based on image translation between original modalities and various feature matching algorithms. The proposed solution not only provides better quality of matching, but is also more versatile. It enables the use of ready-made RoMa and DeDoDe models, pre-trained for regular images, without retraining for a new modality, while maintaining high-quality matching of optical and SAR images.

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$p$-Adic Polynomial Regression as Alternative to Neural Network for Approximating $p$-Adic Functions of Many Variables

Mar 30, 2025

This work addresses the problem of high-precision uniform approximation of multivariate $p$-adic continuous functions $f: mathbb{Z}_p^n o mathbb{Z}_p$. We propose an analytic polynomial regression model based on linear superpositions of univariate $p$-adic basis functions. Unlike black-box $p$-adic neural networks, our approach yields the first explicit, interpretable, and lightweight framework capable of achieving arbitrary-precision uniform approximation. The core contribution lies in leveraging $p$-adic analysis and continuous function decomposition theory to reduce multivariate approximation to linear modeling over univariate bases, with rigorous theoretical guarantees on approximation capacity. Moreover, we provide physically meaningful parameter interpretations and a numerically feasible training procedure. Experiments demonstrate that the model achieves approximation accuracy and generalization performance comparable to state-of-the-art deep methods, while maintaining low computational complexity. This work establishes a new theoretical foundation and practical paradigm for $p$-adic machine learning.

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Recent publications

Latest Papers

Matching of SAR and optical images based on transformation to shared modality

Feb 13, 2026

Significant differences in optical images and Synthetic Aperture Radar (SAR) images are caused by fundamental differences in the physical principles underlying their acquisition by Earth remote sensing platforms. These differences make precise image matching (co-registration) of these two types of images difficult. In this paper, we propose a new approach to image matching of optical and SAR images, which is based on transforming the images to a new modality. The new image modality is common to both optical and SAR images and satisfies the following conditions. First, the transformed images must have an equal pre-defined number of channels. Second, the transformed and co-registered images must be as similar as possible. Third, the transformed images must be non-degenerate, meaning they must preserve the significant features of the original images. To further match images transformed to this shared modality, we train the RoMa image matching model, which is one of the leading solutions for matching of regular digital photographs. We evaluated the proposed approach on the publicly available MultiSenGE dataset containing both optical and SAR images. We demonstrated its superiority over alternative approaches based on image translation between original modalities and various feature matching algorithms. The proposed solution not only provides better quality of matching, but is also more versatile. It enables the use of ready-made RoMa and DeDoDe models, pre-trained for regular images, without retraining for a new modality, while maintaining high-quality matching of optical and SAR images.

0 citationsRead paper

$p$-Adic Polynomial Regression as Alternative to Neural Network for Approximating $p$-Adic Functions of Many Variables

Mar 30, 2025

This work addresses the problem of high-precision uniform approximation of multivariate $p$-adic continuous functions $f: mathbb{Z}_p^n o mathbb{Z}_p$. We propose an analytic polynomial regression model based on linear superpositions of univariate $p$-adic basis functions. Unlike black-box $p$-adic neural networks, our approach yields the first explicit, interpretable, and lightweight framework capable of achieving arbitrary-precision uniform approximation. The core contribution lies in leveraging $p$-adic analysis and continuous function decomposition theory to reduce multivariate approximation to linear modeling over univariate bases, with rigorous theoretical guarantees on approximation capacity. Moreover, we provide physically meaningful parameter interpretations and a numerically feasible training procedure. Experiments demonstrate that the model achieves approximation accuracy and generalization performance comparable to state-of-the-art deep methods, while maintaining low computational complexity. This work establishes a new theoretical foundation and practical paradigm for $p$-adic machine learning.

0 citationsRead paper