Graph Spatio-Spectral Total Variation Model for Hyperspectral Image Denoising

The spatio-spectral total variation (SSTV) model has been widely used as an effective regularization of hyperspectral images (HSI) for various applications such as mixed noise removal. However, since SSTV computes local spatial differences uniformly, it is difficult to remove noise while preserving complex spatial structures with fine edges and textures, especially in situations of high noise intensity. To solve this problem, we propose a new TV-type regularization called Graph-SSTV (GSSTV), which generates a graph explicitly reflecting the spatial structure of the target HSI from noisy HSIs and incorporates a weighted spatial difference operator designed based on this graph. Furthermore, we formulate the mixed noise removal problem as a convex optimization problem involving GSSTV and develop an efficient algorithm based on the primal-dual splitting method to solve this problem. Finally, we demonstrate the effectiveness of GSSTV compared with existing HSI regularization models through experiments on mixed noise removal. The source code will be available at https://www.mdi.c.titech.ac.jp/publications/gsstv.Comment: Accepted to IEEE Geoscience and Remote Sensing Letters. The code is available at https://www.mdi.c.titech.ac.jp/publications/gsst

Approximate Message Passing in Coded Aperture Snapshot Spectral Imaging

We consider a compressive hyperspectral imaging reconstruction problem, where three-dimensional spatio-spectral information about a scene is sensed by a coded aperture snapshot spectral imager (CASSI). The approximate message passing (AMP) framework is utilized to reconstruct hyperspectral images from CASSI measurements, and an adaptive Wiener filter is employed as a three-dimensional image denoiser within AMP. We call our algorithm "AMP-3D-Wiener." The simulation results show that AMP-3D-Wiener outperforms existing widely-used algorithms such as gradient projection for sparse reconstruction (GPSR) and two-step iterative shrinkage/thresholding (TwIST) given the same amount of runtime. Moreover, in contrast to GPSR and TwIST, AMP-3D-Wiener need not tune any parameters, which simplifies the reconstruction process.Comment: to appear in Globalsip 201

A Constrained Convex Optimization Approach to Hyperspectral Image Restoration with Hybrid Spatio-Spectral Regularization

We propose a new constrained optimization approach to hyperspectral (HS) image restoration. Most existing methods restore a desirable HS image by solving some optimization problem, which consists of a regularization term(s) and a data-fidelity term(s). The methods have to handle a regularization term(s) and a data-fidelity term(s) simultaneously in one objective function, and so we need to carefully control the hyperparameter(s) that balances these terms. However, the setting of such hyperparameters is often a troublesome task because their suitable values depend strongly on the regularization terms adopted and the noise intensities on a given observation. Our proposed method is formulated as a convex optimization problem, where we utilize a novel hybrid regularization technique named Hybrid Spatio-Spectral Total Variation (HSSTV) and incorporate data-fidelity as hard constraints. HSSTV has a strong ability of noise and artifact removal while avoiding oversmoothing and spectral distortion, without combining other regularizations such as low-rank modeling-based ones. In addition, the constraint-type data-fidelity enables us to translate the hyperparameters that balance between regularization and data-fidelity to the upper bounds of the degree of data-fidelity that can be set in a much easier manner. We also develop an efficient algorithm based on the alternating direction method of multipliers (ADMM) to efficiently solve the optimization problem. Through comprehensive experiments, we illustrate the advantages of the proposed method over various HS image restoration methods including state-of-the-art ones.Comment: 20 pages, 4 tables, 10 figures, submitted to MDPI Remote Sensin