Coupled Tensor Decomposition for Hyperspectral and Multispectral Image Fusion With Inter-Image Variability

Abstract

Coupled tensor approximation has recently emerged as a promising approach for the fusion of hyperspectral and multispectral images, reconciling state of the art performance with strong theoretical guarantees. However, tensor-based approaches previously proposed assume that the different observed images are acquired under exactly the same conditions. A recent work proposed to accommodate spectral variability in the image fusion problem using a matrix factorizationbased formulation, but did not account for spatially-localized variations. Moreover, it lacks theoretical guarantees and has a high associated computational complexity. In this paper, we consider the image fusion problem while accounting for both spatially and spectrally localized changes in an additive model. We first study how the general identifiability of the model is impacted by the presence of such changes. Then, assuming that the high-resolution image and the variation factors admit a Tucker decomposition, two new algorithms are proposedone purely algebraic, and another based on an optimization procedure. Theoretical guarantees for the exact recovery of the high-resolution image are provided for both algorithms. Experimental results show that the proposed method outperforms state-of-the-art methods in the presence of spectral and spatial variations between the images, at a smaller computational cost.

Hyperspectral Super-resolution Accounting for Spectral Variability: Coupled Tensor LL1-Based Recovery and Blind Unmixing of the Unknown Super-resolution Image

“…As a result, in this paper, we adopt a more general approach. As in [6], we consider two different SRIs Z ∈ R I×J×K and Z ∈ R I×J×K , underlying the HSI and MSI, respectively.…”

“…In this framework, the HSR problem consists recovering Z ∈ R I×J×K and Ψ ∈ R I×J×K under the assumption of the observation model (2.2)-(2.3). However, the presence of the variability tensor Ψ makes this problem ambiguous [6], as one cannot easily separate Z and Ψ from Z. We recall the following theorem [6]: Theorem 2.1.…”

“…However, the presence of the variability tensor Ψ makes this problem ambiguous [6], as one cannot easily separate Z and Ψ from Z. We recall the following theorem [6]: Theorem 2.1. [6, Theorem 1.a)] Suppose that the HSI and MSI are generated according to (2.3) and that the observation noise is zero (i.e.…”

“…In [6], approaches based on model (2.3) were proposed, using a coupled Tucker approximation. However, due to the non-uniqueness of the Tucker decomposition, the latent multilinear factors were not guaranteed to be unique, and no non-negativity constraints were enforced.…”

“…However, the algorithm in [4] presented high computation times and did not offer any theoretical guarantees. In [6], two tensor-based algorithms based on the Tucker decom-This manuscript is for review purposes only. position were proposed, accounting for spatially and spectrally-localized changes between the HSI and MSI.…”