  Deep learning (DL) based hyperspectral images (HSIs) denoising approaches
directly learn the nonlinear mapping between observed noisy images and
underlying clean images. They normally do not consider the physical
characteristics of HSIs, therefore making them lack of interpretability that is
key to understand their denoising mechanism.. In order to tackle this problem,
we introduce a novel model guided interpretable network for HSI denoising.
Specifically, fully considering the spatial redundancy, spectral low-rankness
and spectral-spatial properties of HSIs, we first establish a subspace based
multi-dimensional sparse model. This model first projects the observed HSIs
into a low-dimensional orthogonal subspace, and then represents the projected
image with a multidimensional dictionary. After that, the model is unfolded
into an end-to-end network named SMDS-Net whose fundamental modules are
seamlessly connected with the denoising procedure and optimization of the
model. This makes SMDS-Net convey clear physical meanings, i.e., learning the
low-rankness and sparsity of HSIs. Finally, all key variables including
dictionaries and thresholding parameters are obtained by the end-to-end
training. Extensive experiments and comprehensive analysis confirm the
denoising ability and interpretability of our method against the
state-of-the-art HSI denoising methods.
