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

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

Robust Constrained Hyperspectral Unmixing Using Reconstructed-Image Regularization

Hyperspectral (HS) unmixing is the process of decomposing an HS image into material-specific spectra (endmembers) and their spatial distributions (abundance maps). Existing unmixing methods have two limitations with respect to noise robustness. First, if the input HS image is highly noisy, even if the balance between sparse and piecewise-smooth regularizations for abundance maps is carefully adjusted, noise may remain in the estimated abundance maps or undesirable artifacts may appear. Second, existing methods do not explicitly account for the effects of stripe noise, which is common in HS measurements, in their formulations, resulting in significant degradation of unmixing performance when such noise is present in the input HS image. To overcome these limitations, we propose a new robust hyperspectral unmixing method based on constrained convex optimization. Our method employs, in addition to the two regularizations for the abundance maps, regularizations for the HS image reconstructed by mixing the estimated abundance maps and endmembers. This strategy makes the unmixing process much more robust in highly-noisy scenarios, under the assumption that the abundance maps used to reconstruct the HS image with desirable spatio-spectral structure are also expected to have desirable properties. Furthermore, our method is designed to accommodate a wider variety of noise including stripe noise. To solve the formulated optimization problem, we develop an efficient algorithm based on a preconditioned primal-dual splitting method, which can automatically determine appropriate stepsizes based on the problem structure. Experiments on synthetic and real HS images demonstrate the advantages of our method over existing methods.Comment: Submitted to IEEE Transactions on Geoscience and Remote Sensin

Robust Hyperspectral Image Fusion with Simultaneous Guide Image Denoising via Constrained Convex Optimization

The paper proposes a new high spatial resolution hyperspectral (HR-HS) image estimation method based on convex optimization. The method assumes a low spatial resolution HS (LR-HS) image and a guide image as observations, where both observations are contaminated by noise. Our method simultaneously estimates an HR-HS image and a noiseless guide image, so the method can utilize spatial information in a guide image even if it is contaminated by heavy noise. The proposed estimation problem adopts hybrid spatio-spectral total variation as regularization and evaluates the edge similarity between HR-HS and guide images to effectively use apriori knowledge on an HR-HS image and spatial detail information in a guide image. To efficiently solve the problem, we apply a primal-dual splitting method. Experiments demonstrate the performance of our method and the advantage over several existing methods.Comment: Accepted to IEEE Transactions on Geoscience and Remote Sensin

Improved Quasi-Recurrent Neural Network for Hyperspectral Image Denoising

Hyperspectral image is unique and useful for its abundant spectral bands, but it subsequently requires extra elaborated treatments of the spatial-spectral correlation as well as the global correlation along the spectrum for building a robust and powerful HSI restoration algorithm. By considering such HSI characteristics, 3D Quasi-Recurrent Neural Network (QRNN3D) is one of the HSI denoising networks that has been shown to achieve excellent performance and flexibility. In this paper, we show that with a few simple modifications, the performance of QRNN3D could be substantially improved further. Our modifications are based on the finding that through QRNN3D is powerful for modeling spectral correlation, it neglects the proper treatment between features from different sources and its training strategy is suboptimal. We, therefore, introduce an adaptive fusion module to replace its vanilla additive skip connection to better fuse the features of the encoder and decoder. We additionally identify several important techniques to further enhance the performance, which includes removing batch normalization, use of extra frequency loss, and learning rate warm-up. Experimental results on various noise settings demonstrate the effectiveness and superior performance of our method.Comment: technical repor