Hyperspectral images (HSIs) are generally susceptible to various noise, such as Gaussian and stripe noise. Recently, numerous denoising algorithms have been proposed to recover the HSIs. However, those approaches cannot use spectral information efficiently and suffer from the weakness of stripe noise removal. Here, we propose a tensor decomposition method with two different constraints to remove the mixed noise from HSIs. For a HSI cube, we first employ the tensor singular value decomposition (t-SVD) to effectively preserve the low-rank information of HSIs. Considering the continuity property of HSIs spectra, we design a simple smoothness constraint by using Tikhonov regularization for tensor decomposition to enhance the denoising performance. Moreover, we also design a new unidirectional total variation (TV) constraint to filter the stripe noise from HSIs. This strategy will achieve better performance for preserving images details than original TV models. The developed method is evaluated on both synthetic and real noisy HSIs, and shows the favorable results.

Compressive spectral imaging (CSI) systems capture the 3D spatiospectral data by measuring the 2D compressed focal plane array (FPA) coded projection with the help of reconstruction algorithms exploiting the sparsity of signals. However, the contradiction between the multi-dimension of the scenes and the limited dimension of the sensors has limited improvement of recovery performance. In order to solve the problem, a novel CSI system based on a coded aperture snapshot spectral imager, RGB-CASSI, is proposed, which has two branches, one for CASSI, another for RGB images. In addition, considering that conventional reconstruction algorithms lead to oversmoothing, a RGB-guided low-rank (RGBLR) method for compressive hyperspectral image reconstruction based on compressed sensing and coded aperture spectral imaging system is presented, in which the available additional RGB information is used to guide the reconstruction and a low-rank regularization for compressive sensing and a non-convex surrogate of the rank is also used instead of nuclear norm for seeking a preferable solution. Experiments show that the proposed algorithm performs better in both PSNR and subjective effects compared with other state-of-art methods.

The Retinex theory assumes that large intensity changes correspond to reflectance edges, while smoothly-varying regions are due to shading. Some algorithms based on the theory adopt simple thresholding schemes and achieve adequate results for reflectance estimation. In this paper, we present a practical reflectance estimation technique for hyperspectral images. Our method is realized simply by thresholding singular values of a matrix calculated from scaled pixel values. In the method, we estimate the reflectance image by measuring spectral similarity between two adjacent pixels. We demonstrate that our thresholding scheme effectively estimates the reflectance and outperforms the Retinex-based thresholding. In particular, our methods can precisely distinguish edges caused by reflectance change and shadows.

Restoration is an important area in improving the visual quality, and lays the foundation for accurate object detection or terrain classification in image analysis. In this paper, we introduce Beta process priors into hierarchical sparse Bayesian learning for recovering underlying degraded hyperspectral images (HSI), including suppressing the various noises and inferring the missing data. The proposed method decomposes the HSI into the weighted summation of the dictionary elements, Gaussian noise term and sparse noise term. With these, the latent information and the noise characteristics of HSI can be well learned and represented. Solved by Gibbs sampler, the underlying dictionary and the noise can be efficiently predicted with no tuning of any parameters. The performance of the proposed method is compared with state-of-the-art ones and validated on two hyperspectral datasets, which are contaminated with the Gaussian noises, impulse noises, stripes and dead pixel lines, or with a large number of data missing uniformly at random. The visual and quantitative results demonstrate the superiority of the proposed method.

Using traditional single-layer dictionary learning methods, it is difficult to reveal the complex structures hidden in the hyperspectral images. Motivated by deep learning technique, a deep dictionary learning approach is proposed for hyperspectral image denoising, which consists of hierarchical dictionary learning, feature denoising and fine-tuning. Hierarchical dictionary learning is helpful for uncovering the hidden factors in the spectral dimension, and fine-tuning is beneficial for preserving the spectral structure. Experiments demonstrate the effectiveness of the proposed approach.