Abstract: Due to various factors,e.g.,thermal electronics,dark current,and stochastic error of photocounting in an imaging process,hyperspectral images(HSI)are inevitably corrupted by different types of noise during the acquisition and transmission process.For effective noise removal,in this paper,we attempt to extend the annihilating filter for the HSI community.Specifically,a new method based on the structural matrix recovery is presented.First,benefiting from the correlation of different spectral bands and the smoothness of local spatial neighborhood,the image patches are hankelized to be a structural low-rank matrix;Then considering that the linear hankelization does not destroy the sparse attribution of the impulse noise,sparsity prior can be employed as a constraint;Finally,by using the truncated nuclear norm and group sparse norm as the surrogates of the original low-rank and sparse function,our final model is formed by two prior conditions and be solved via the well-known ADMM optimization algorithm.The whole image denoising procedure involves three main steps,i.e.,the decomposition of input image into overlapped patches,the block-wise estimates for each patch,and the recovery of the whole image.The experimental results show that our proposed method is superior to other state-of-the-art methods both visually and quantitative indices,such as peak signal to noise ratio(PSNR),structural similarity index measure(SSIM)and spectral angle distance(SAD).