Gradient-singular value duality and its application in multi-focus image fusion via HOSVD and CNN

Multi-focus image fusion aims to integrate partially focused images of the same scene into a single all-in-focus image. However, existing methods face two fundamental challenges: (1) accurately distinguishing focused regions from defocused ones in complex scenes, and (2) preserving sharp edge details and structural coherence in the fused result, as conventional activity measures based on a single feature often fail to capture the full richness of image structures. To address these challenges, this paper proposes a novel multi-focus image fusion framework that integrates high-order singular value decomposition (HOSVD), a gradient-singular value (GSV) activity measure, and a convolutional neural network (CNN). Specifically, HOSVD is employed to capture higher-order structural correlations among image blocks in a fully data-driven manner, enabling precise texture extraction without manual parameter tuning. The proposed GSV measure jointly characterizes local edge strength and global structural saliency by combining directional gradient information with singular value decomposition, effectively distinguishing focused regions from defocused ones and preserving structural coherence. A lightweight CNN is then introduced to perform adaptive deep fusion and reconstruction on the HOSVD-GSV feature representations, generating fused images with enhanced edge details. Extensive experiments on three public multi-focus datasets demonstrate that the proposed method consistently outperforms nine state-of-the-art approaches, achieving superior performance across a comprehensive set of objective metrics, alongside favorable subjective visual quality.