Taylor-Series and Partial-Derivative–Driven Image Processing and Medical CT Analysis Using Optimized Deep Learning Frameworks

Abstract

Existing image processing and medical CT analysis methods often require a lot of computing power and can take a long time. This paper reviews a framework driven by Taylor-series and partial derivatives to improve efficiency and accuracy in image processing and medical image analysis. The Taylor series expansion simplifies complex nonlinear functions into polynomial approximations. Partial differentiation helps detect edges and analyze changes in image intensity. Error approximation measures the difference between exact and estimated solutions, balancing computational speed and image quality. The proposed framework combines Taylor-series-based mathematical transformations with optimized deep learning techniques. This is useful for image enhancement, compression, super-resolution, and automated stroke detection in brain CT images. Experimental results show reduced computational complexity, faster convergence, and better diagnostic accuracy. This demonstrates the effectiveness of Taylor-series-based methods in modern image processing and medical AI systems.

Introduction

The text presents a computational framework that combines Taylor series approximation with deep learning to improve efficiency in image processing and medical imaging tasks, especially CT-based stroke detection.

Modern deep learning and image-processing methods are accurate but computationally expensive. To address this, Taylor series is used to approximate complex nonlinear functions with simpler polynomial expressions, reducing computational cost while maintaining acceptable accuracy. This idea is applied across several domains such as image compression, enhancement, super-resolution, augmented reality, and matrix factorization.

The proposed method, called the Taylor-Series-Based Approximation Framework (TS-AF), first applies Taylor expansion to linearize nonlinear operations, then integrates optimization techniques and deep learning for final prediction. First-, second-, and higher-order Taylor approximations are used depending on the task, balancing speed and accuracy.

Mathematically, image functions are modeled using partial derivatives, allowing local approximation of pixel variations. The framework also includes error estimation to measure the difference between exact and approximated results.

Applications include:

• Image enhancement using second-order Taylor expansion to preserve edges
• Image compression through polynomial approximation of transformations
• Digital image correlation for precise motion estimation
• Super-resolution where Taylor approximation reduces attention complexity
• Matrix factorization optimization using simplified divergence measures

Conclusion

There are no computational efficiencies in existing strategies, which is why the presented framework is motivated. Finally, this paper collates multiple research contributions to prove the effectiveness of Taylor-series-based solutions in different image processing problems. It also proposes a framework for combining Taylor-based image processing methods with Taylor-optimized deep learning models for medical CT image analysis. Using first-order, second-order, and more Taylor expansions to simplify complex nonlinear functions. This way, computation time is reduced without compromising the significant features in an image, like the edges and textures. The proposed Taylor-Series-Based Approximation Framework provides a single mathematical framework that can be used for image compression, enhancement, correlation super-resolution, and matrix factorization. As a result, an approach that combines mathematical approximation with smart optimization and deep learning models provides better speed and accuracy. Overall, the results show that the Taylor series is not just a classical math concept but also a useful and powerful tool for modern image processing and medical AI systems. The combination of partial differentiation and approximation error analysis adds to the mathematical foundation of the proposed Taylor-series-based framework. This approach improves computational efficiency and analytical reliability. Future work may extend this framework to 3D medical image reconstruction and real-time AI-assisted diagnostic systems.

References

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Copyright

Copyright © 2026 Ashwini Vaze, Sanskruti Patil, Ganisha Shiv, Achal Dandhare. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.