Signal Subspace Identification for Incomplete Hyperspectral Image With Applications to Various Inverse Problems

In hyperspectral remote sensing (HRS), signal subspace identification (SSID) is a critical step in many widely renowned HRS algorithms, while the accuracy of the subspace identification relies on the complete information of the data pixels. However, as the sensor arrays would be partially damaged after the satellites are launched, hyperspectral pixels are quite often incompletely acquired. Even for those renowned algorithms, they simply remove those incomplete pixels when computing the hyperspectral signal subspace. Nevertheless, even if some spectral bands of a given incomplete pixel are missing, we intuitively believe that the remaining bands of that pixel should still contribute to the accuracy of the subspace identification. We design a computationally efficient algorithm, termed as subspace identification for incomplete signals of hyperspectral image (SISHY), to utilize the information embedded in those incomplete pixels. To this end, we prove a lemma that allows us to reformulate the algebraic identification problem into an affine geometry problem, thereby allowing us to flexibly add suitable regularizer for better identification result as needed. SISHY judiciously associates the regularized subspace identification problem with a denoising operator, thereby allowing an efficient algorithm implementation and yielding a physically interpretable data matrix completion result as a byproduct. Experiments demonstrate that the SISHY algorithm does improve the efficacy of the subsequent tasks of unmixing, inpainting, and classification.