Spectrally-Spatially Regularized Low-Rank and Sparse Decomposition: A Novel Method for Change Detection in Multitemporal Hyperspectral Images

Change detection (CD) for multitemporal hyperspectral images (HSI) can be approached as classification consisting of two steps, change feature extraction and change identification. This paper is focused on binary classification of the changed and the unchanged samples, which is the essential case of change detection. Meanwhile, it is challenging to extract clean change features from heavily corrupted spectral change vectors (SCV) of multitemporal HSI. The corruptions can be characterized as gross sample-specific errors, i.e., outliers, and small entry-wise noise following Gaussian distribution. To address the issue, this paper proposes a novel Spectrally-Spatially (SS) Regularized Low-Rank and Sparse Decomposition (LRSD) model, denoted by LRSD_SS. It decomposes the SCV into three components, a locally smoothed low-rank matrix for the clean change features, a sparse matrix for the outliers and an error matrix for the small Gaussian noise. The proposed method is effective in change feature extraction and robust to noise corruptions as it exploits the underlying data structures of the SCV, especially local spectral-spatial smoothness. It is also efficient since there is a closed-form solution for the feature component in the optimization problem of LRSD_SS. The experimental results in the paper show that the proposed method outperforms several classic methods which only deal with the spectral domain of image samples, as well as some state-of-the-art methods which use both spectral and spatial informatio