Noise reduction and feature extraction based on low-rank representation and pairwise constraint preserving for hyperspectral images

Feature extraction (FE) methods play a central role in the classification of hyperspectral images (HSIs). However, all traditional FE methods work in original feature space (OFS), OFS may suffer from noise, outliers and poorly discriminative features. This paper presents a feature space enriching technique to address the problems of noise, outliers and poorly discriminative features which may exist in OFS. The proposed method is based on low-rank representation (LRR) with the capability of pairwise constraint preserving (PCP) termed LRR-PCP. LRR-PCP does not change the dimension of OFS and only can be used as an appropriate preprocessing procedure for any classification algorithm or DR methods. The proposed LRR-PCP aims to enrich the OFS and obtain extracted feature space (EFS) which results in features richer than OFS. The problems of noise and outliers can be decreased using LRR. But, LRR cannot preserve the intrinsic local structure of the original data and only capture the global structure of data. Therefore, two additional penalty terms are added into the objective function of LRR to keep the local discriminative ability and also preserve the data diversity. LRR-PCP method not only can be used in supervised learning but also in unsupervised and semi-supervised learning frameworks. The effectiveness of LRR-PCP is investigated on three HSI data sets using some existing DR methods and as a denoising procedure before the classification task. All experimental results and quantitative analysis demonstrate that applying LRR-PCP on OFS improves the performance of the classification and DR methods in supervised, unsupervised, and semi-supervised conditions.