Tensor Robust CUR for Compression and Denoising of Hyperspectral Data

Hyperspectral images are often contaminated with noise which degrades the quality of data. Recently, tensor robust principal component analysis (TRPCA) has been utilized to remove noise from hyperspectral images, improving classification accuracy. However, the high dimensionality and size of hyperspectral data present computational challenges both in terms of storage and processing power, especially in the case of TRPCA. The situation is exacerbated when the data is too large to fit in available memory. In this paper, we propose a tensor-robust CUR (TRCUR) algorithm for hyperspectral data compression and denoising. We heavily downsample the input hyperspectral image to form small subtensors; and perform TRPCA on the small subtensors. The desired hyperspectral image is recovered by combining the low-rank solution of the subtensors using tensor CUR reconstruction. We provide a theoretical guarantee to show that the desired low-rank tensor can be exactly recovered using our proposed TRCUR method. Numerical experiments indicate that our method is up to 14 times faster than performing TRPCA on the original input data while maintaining the classification accuracy.