An Adaptive Hybrid Conjugate Gradient Algorithm Based on Curvature and Descent for Image Denoising

Abstract

A recently proposed refined conjugate-gradient update, known as BBP, speeds up the restoration of images damaged by impulse noise while matching the quality of older approaches. Its main shortcoming is rigidity; the same update rule is applied at every step, regardless of how the problem's local behaviour shifts as the optimization proceeds. This paper introduces an adaptive hybrid scheme that blends BBP with the Hager-Zhang update through a mixing weight recalculated at every iteration from simple measures of local curvature reliability and descent quality. A built-in safeguard keeps every search direction genuinely descending, which supports a global convergence guarantee that holds no matter how the mixing weight behaves. Tested on salt-and-pepper noise removal across three images and six noise levels, the combined update cuts computational cost substantially at no loss in quality, and the safeguard adds virtually no overhead.