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

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.