We propose a three-dimensional (3-D) denoising approach and coding scheme. The suggested denoising algorithm is taking full advantage of the supplied volumetric data by decomposing the original hyperspectral imagery into individual subspaces, applying an orthogonal isotropic 3-D divergence-free wavelet transformation. The delineated capability of hierarchically structured wavelet coefficients improves the efficiency of the suggested denoising algorithm and effectively preserves the finest details and the relevant image features by emphasizing a nonlocal similarity and spectral-spatial structure of hyperspectral imagery into sparse representation. The proposed method is evaluated using spectral angle distance for a ground-truth spectral dataset and by classification accuracies using water quality indices, which are particularly sensitive to the presence of noise. The reported results are based on a real dataset, presenting three different airborne hyperspectral systems: AHS, CASI-1500i, and AisaEAGLE. Several qualitative and quantitative evaluation measures are applied to validate the ability of the suggested method for noise reduction and image quality enhancement. Experimental results demonstrate that the proposed denoising algorithm achieves better performance when applied on the suggested wavelet transformation compared with other examined noise reduction and hyperspectral image restoration techniques.