  Hyperspectral images are typically composed of hundreds of narrow and
contiguous spectral bands, each containing information about the material
composition of the imaged scene. However, these images can be affected by
various sources of noise, distortions, or data losses, which can significantly
degrade their quality and usefulness. To address these problems, we introduce
two novel self-supervised Hyperspectral Images (HSI) inpainting algorithms: Low
Rank and Sparsity Constraint Plug-and-Play (LRS-PnP), and its extension
LRS-PnP-DIP, which features the strong learning capability, but is still free
of external training data. We conduct the stability analysis under some mild
assumptions which guarantees the algorithm to converge. It is specifically very
helpful for the practical applications. Extensive experiments demonstrate that
the proposed solution is able to produce visually and qualitatively superior
inpainting results, achieving state-of-the-art performance. The code for
reproducing the results is available at
\url{https://github.com/shuoli0708/LRS-PnP-DIP}.
