Fusion of Hyperspectral and Multispectral Images With Sparse and Proximal Regularization

Fusion of hyperspectral and multispectral imagery data is utilized to reconstruct a super-resolution image with high spectral and spatial resolution, which plays a significant role in remote sensing image processing. Conversely, hyperspectral and multispectral data can be modeled as two low-dimensional subspaces by respectively spatially and spectrally degrading the desired image. A representative method is called coupled non-negative matrix factorization (CNMF) based on a Gaussian observation model, but it is an ill-posed inverse problem. In addition, from the perspective of matrix factorization, the matrixing process of hyperspectral and multispectral cube data generally results in the loss of structural information and performance degradation. To address these issues, this article proposes a proximal minimum-volume expression to regularize the convex simplex, enclosing all reconstructed image pixels instead of low-dimensional subspace data. Then, we incorporate sparse and proximal regularizers into the original CNMF to reformulate the fusion problem as a dynamical system via proximal alternating optimization. Finally, the alternating direction method of multipliers is adopted to split the variables for the closed-form solutions that are further reduced in computational complexity. The experimental results show that the proposed algorithm in this paper performs better than the state-of-the-art fusion methods in most cases, which verifies the effectiveness and efficiency of this proposed algorithm in yielding high-fidelity reconstructed images.