VSJE: A Variational-Based Spatial–Spectral Joint Enhancement Method for Underwater Image

Underwater imaging suffers from significant degradation due to scattering by suspended particles, selective absorption by the medium, and depth-dependent noise, leading to issues such as contrast reduction, color distortion, and blurring. Existing enhancement methods typically address only one aspect of these problems, relying on unrealistic assumptions of uniform noise, and fail to jointly handle the spatially heterogeneous noise and spectral channel attenuation. To address these challenges, we propose the variational-based spatial–spectral joint enhancement method (VSJE). This method is based on the physical principles of underwater optical imaging and constructs a depth-aware noise heterogeneity model to accurately capture the differences in noise intensity between near and far regions. Additionally, we propose a channel-sensitive adaptive regularization mechanism based on multidimensional statistics to accommodate the spectral attenuation characteristics of the red, green, and blue channels. A unified variational energy function is then formulated to integrate noise suppression, data fidelity, and color consistency constraints within a collaborative optimization framework, where the depth-aware noise model and channel-sensitive regularization serve as the core adaptive components of the variational formulation. This design enables the joint restoration of multidimensional degradation in underwater images by leveraging the variational framework’s capability to balance multiple enhancement objectives in a mathematically rigorous manner. Experimental results using the UIEBD-VAL dataset demonstrate that VSJE achieves a URanker score of 2.4651 and a UICM score of 9.0740, representing a 30.9% improvement over the state-of-the-art method GDCP in the URanker metric—a key indicator for evaluating the overall visual quality of underwater images. VSJE exhibits superior performance in metrics related to color uniformity (UICM), perceptual quality (CNNIQA, PAQ2PIQ), and overall visual ranking (URanker).