Robust Hyperspectral Inpainting via Low-Rank Regularized Untrained Convolutional Neural Network

Abstract

Over the past decade, many low-rank models, factorizations, or approximations have been applied to the restoration of hyperspectral images (HSIs) (e.g., denoising, inpainting, and super-resolution) from their incomplete and/or noisy measurements. Recently, deep learning (DL) has been shown to be a powerful method for solving inverse problems (including HSI restoration), but a large amount of training data is required. Since this is not possible for HSIs, unlike red green blue (RGB) images, in this work, a novel unsupervised framework for hyperspectral inpainting (HI) is proposed that can be implemented using an untrained convolutional neural network (CNN) for deep image prior (DIP), together with a recently reported differentiable regularization for the data rank and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{2}$ </tex-math></inline-formula> -norm squared loss function. Based on the proposed framework, we come up with a novel HI algorithm [denoted as deep low-rank hyperspectral inpainting (DLRHyIn)] and a robust DLRHyIn (denoted as R-DLRHyIn) which is robust against outliers, where the latter differs from the former only in the Huber loss function (HLF) (which has been justified robust to mixed noise) used instead. Then some simulation results and real-data experiments are provided to demonstrate the effectiveness of the proposed DLRHyIn and R-DLRHyIn. Finally, we draw some conclusions.