Hyperspectral Image Denoising via $L_{0}$ Regularized Low-Rank Tucker Decomposition
Xin Tian, Kun Xie, Hanling Zhang
Abstract
This paper studies the mixed noise removal problem for hyperspectral images (HSIs), which often suffer from Gaussian noise and sparse noise. Conventional denoising models mainly employ the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{1}$</tex-math></inline-formula> -norm-based regularizers to remove sparse noise and ensure piecewise smoothness. However, the denoising performance is poor for highly structured images with severe noise since the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{1}$</tex-math></inline-formula> -norm over-penalizes large entries. To tackle this limitation, we propose a denoising model that combines tensor decomposition with two kinds of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{0}$</tex-math></inline-formula> -norm-based regularizers. Firstly, we use low-rank Tucker decomposition with the Stiefel manifold to characterize the global correlation of HSIs. Then, we utilize the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{0}$</tex-math></inline-formula> -norm to leverage the intrinsic sparsity information of the corruption domain, thereby enhancing the effectiveness of sparse noise removal. Simultaneously, we introduce a weighted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{0}$</tex-math></inline-formula> -norm regularizer on the gradient of each pixel to promote the local spectral-spatial smoothness. To solve the proposed model, we design a hard-thresholding-based alternating direction method of multipliers (ADMM) algorithm. Instead of spending time to find a proper rank in advance, we adopt a rank-increasing scheme to dynamically adjust the tensor rank during the optimization procedure. In this way, our algorithm avoids the rank selection burden and improves computational efficiency. Finally, we test the proposed method on both synthetic and real datasets. Numerical results demonstrate its superiority, especially, the improvements of our method over the best-compared results up to 2.07dB for mixed noise removal.