Hankel Tensor Subspace Representation for Remotely Sensed Image Fusion

Remotely sensed image fusion is an economical and effective means to acquire super-resolution reconstruction of hyperspectral data, which overcomes the inherent limitations of single-sensor systems. As an illposed inverse problem, however, current multisensor data fusion faces many challenges. Exactly, traditional matrix-factorization-based algorithms often result in the loss of cubic structure knowledge in hyperspectral data, while deep neural networks are susceptible to noise accumulation and lack of large-scale labeled data. Moreover, tensor-based approaches still suffer from large computation and the uncertainty of tensor rank especially in noise-polluted environments, even though it can keep cubic structure. To tackle these challenges, this article reformulates a novel image fusion model by incorporating Hankel tensor subspace representation (HTSR) for quality improvement of reconstruction images. Initially, after tensor decomposition, each factor component is mapped separately into a high-dimensional Hankel subspace by delayed embedding for exploring the underlying prior features. Low-rank regularization is then imposed on the Hankel tensor to address the rank uncertainty and suppress noise-related distortion, thereby reducing the computational complexity of exact tensor rank. Furthermore, exerting <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{1}$</tex-math></inline-formula> norm on core tensor is conducted to promote the sparsity for generalization enhancement. In the end, vector-tensor operators, as well as alternating optimization, are leveraged to design an efficient solver for computation reduction. Experimental tests on several real datasets demonstrate that the proposed fusion model significantly achieves better performance in super-resolution reconstruction and noise removal than the representative benchmark methods, which also verifies the validation of Hankel tensor representation and regularization.