Trustworthy multitask image restoration with an adaptive radial basis function framework: spectral features and neural-driven shape parameter optimization

Xiaolu Liu; Jian Sun; Ruxuan Gao; Xiaolu Liu; Jian Sun; Ruxuan Gao

doi:10.3934/math.20251354

AIMS Mathematics

2025, Volume 10, Issue 12: 30851-30878. doi: 10.3934/math.20251354

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Research article

Trustworthy multitask image restoration with an adaptive radial basis function framework: spectral features and neural-driven shape parameter optimization

1.
College of Electronic Information and Control Engineering, Beijing University of Technology, Beijing 100124, China
2.
School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China
3.
Department of Industrial Engineering, Tsinghua University, Beijing 100084, China

Received: 25 October 2025 Revised: 12 December 2025 Accepted: 16 December 2025 Published: 30 December 2025
MSC : 65D05, 68T07

Image restoration is essential for computer vision and medical imaging yet faces challenges from complex degradations, motivating the need for unified multitask frameworks that handle diverse tasks simultaneously. This paper proposed an adaptive radial basis function (RBF) framework designed to achieve high-fidelity restoration across super-resolution, inpainting, denoising, deraining, dehazing, and deshadowing. The method employed Fourier decomposition for spectral feature extraction, an improved random walk algorithm for offline optimal shape parameter labeling, and an Adaptive Moment Estimation-optimized Back Propagation neural network (Adam-BP) for online prediction of the multiquadric shape parameter $c_{\text{opt}}$. A key contribution was the degradation-aware spectral selection mechanism, which automatically adapted RBF kernel sharpness based on frequency content, enabling sharper kernels for resolution-critical tasks and smoother kernels for noise-dominated scenarios. This implicit mechanism, supported by theoretical guarantees of existence, uniqueness, strict convexity, and Lipschitz continuity, facilitated fully automated parameter selection without manual tuning. Experiments on natural and medical images confirmed the framework's effectiveness, with efficient inference times and superior performance over baselines.
- trustworthy image restoration,
- multitask image processing,
- adaptive radial basis function,
- spectral feature extraction,
- neural network optimization
Citation: Xiaolu Liu, Jian Sun, Ruxuan Gao. Trustworthy multitask image restoration with an adaptive radial basis function framework: spectral features and neural-driven shape parameter optimization[J]. AIMS Mathematics, 2025, 10(12): 30851-30878. doi: 10.3934/math.20251354

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Abstract

Image restoration is essential for computer vision and medical imaging yet faces challenges from complex degradations, motivating the need for unified multitask frameworks that handle diverse tasks simultaneously. This paper proposed an adaptive radial basis function (RBF) framework designed to achieve high-fidelity restoration across super-resolution, inpainting, denoising, deraining, dehazing, and deshadowing. The method employed Fourier decomposition for spectral feature extraction, an improved random walk algorithm for offline optimal shape parameter labeling, and an Adaptive Moment Estimation-optimized Back Propagation neural network (Adam-BP) for online prediction of the multiquadric shape parameter $c_{\text{opt}}$. A key contribution was the degradation-aware spectral selection mechanism, which automatically adapted RBF kernel sharpness based on frequency content, enabling sharper kernels for resolution-critical tasks and smoother kernels for noise-dominated scenarios. This implicit mechanism, supported by theoretical guarantees of existence, uniqueness, strict convexity, and Lipschitz continuity, facilitated fully automated parameter selection without manual tuning. Experiments on natural and medical images confirmed the framework's effectiveness, with efficient inference times and superior performance over baselines.

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