Exploring Nonlocal Group Sparsity Under Transform Learning for Hyperspectral Image Denoising

Hyperspectral image (HSI) denoising has been regarded as an effective and economical preprocessing step in data subsequent applications. Recent nonlocal low-rank approximation on each full band patch group has demonstrated their superiority for HSI denoising. These methods, however, directly design low-rank regularization to the grouped patch image itself (i.e., original domain), which ignores the spatial information of the grouped patch image and cannot explore the potential structure. To address these issues, this article proposes a nonlocal group sparsifying transform learning (dubbed TLNLGS) method for HSI denoising. Motivated by the global spectral correlation in the HSI, we first impose a certain low-dimensional subspace hypothesis over the HSI to prevent the heavy computation burden with the spectral band increases, and then explore a discriminatively intrinsic nonlocal group sparse prior of the reduced image by the transform model. The learned group sparse prior can not only excavate the nonlocal self-similarity as recent nonlocal low-rank approximation methods but also preserve the local spatial smooth structure of the image. Moreover, compared with the fixed transform domain (e.g., gradient and discrete cosine transformation domains), the transform learning scheme can improve the sparse representation ability. An efficient block coordinate descent (BCD) algorithm is developed to solve the proposed model. Extensive experiments, including the simulated and real HSI datasets, indicate the superiority of the proposed TLNLGS method over the state-of-the-art HSI denoising approaches.