ABSTRACT
We present double random projection methods for reconstruction of imaging data. The methods draw upon recent results in the random projection literature, particularly on low-rank matrix approximations, and the reconstruction algorithm has only two simple and noniterative steps, while the reconstruction error is close to the error of the optimal low-rank approximation by the truncated singular-value decomposition. We extend the often-required symmetric distributions of entries in a random-projection matrix to asymmetric distributions, which can be more easily implementable on imaging devices. Experimental results are provided on the subsampling of natural images and hyperspectral images, and on simulated compressible matrices. Comparisons with other random projection methods are also provided.
ABSTRACT
An important and well-studied problem in hyperspectral image data applications is to identify materials present in the object or scene being imaged and to quantify their abundance in the mixture. Due to the increasing quantity of data usually encountered in hyperspectral datasets, effective data compression is also an important consideration. In this paper, we develop novel methods based on tensor analysis that focus on all three of these goals: material identification, material abundance estimation, and data compression. Test results are reported in all three perspectives.
