Performance Bounds for Coupled CP Model in the Framework of Hyperspectral Super-Resolution

We derive the constrained Cramér-Rao bounds for a coupled CP model with linear constraints applied to the hyperspectral super-resolution problem. For this problem, we consider two tensors representing low-resolution hyperspectral and multispectral images. In a practical measurement setup, white Gaussian noise sequences are added to each tensor with different variances. The coupling constraints are expressed between the factor matrices of the canonical polyadic model for each tensor. We show that the estimator given by the coupled alternating least squares algorithm achieves the bounds for given Signal-to-Noise Ratios, but requires the knowledge of the ratio of variances of the additive Gaussian noise sequences on each tensor.