Scalable low dimensional manifold model in the reconstruction of noisy and incomplete hyperspectral images
This work addresses reconstruction challenges in hyperspectral imaging, which is incremental as it builds on existing manifold-based methods with scalability improvements.
The paper tackled the problem of reconstructing noisy and incomplete hyperspectral images by proposing a scalable low-dimensional manifold model, resulting in superior speed and accuracy in numerical experiments.
We present a scalable low dimensional manifold model for the reconstruction of noisy and incomplete hyperspectral images. The model is based on the observation that the spatial-spectral blocks of a hyperspectral image typically lie close to a collection of low dimensional manifolds. To emphasize this, the dimension of the manifold is directly used as a regularizer in a variational functional, which is solved efficiently by alternating direction of minimization and weighted nonlocal Laplacian. Unlike general 3D images, the same similarity matrix can be shared across all spectral bands for a hyperspectral image, therefore the resulting algorithm is much more scalable than that for general 3D data. Numerical experiments on the reconstruction of hyperspectral images from sparse and noisy sampling demonstrate the superiority of our proposed algorithm in terms of both speed and accuracy.