Adaptive thresholding HOSVD with rearrangement of tensors for image denoising

Image denoising is a widely used approach in the field of image processing, which restores image more accurately. In particular, higher-order singular value decomposition (HOSVD) algorithm is a prominent algorithm for image denoising. However, traditional HOSVD transform utilizes the fixed threshold to truncate the small transform coefficients under the condition of a given tensor. Thus, some intrinsic properties of the tensor are ignored. In this paper, we propose an adaptive thresholding HOSVD with rearrangement of tensors, called ATH-HOSVD. First, the tensor-based HOSVD transform is employed to exploit the nonlocal tensor property. Second, we consider the spatial distribution of elements in the core tensors and adopt the indices of transform coefficients to produce adaptive threshold. Finally, in order to improve the sparsity of tensors, a rearrangement of tensors based on the amplitude sorting and Hilbert space-filling curve is integrated into the scheme of adaptive thresholding HOSVD. Various experiments on natural images are reported to not only demonstrate the effectiveness of the proposed ATH-HOSVD method, but also show its competitive speed.