Separation Between Anomalous Targets and Background Based on the Decomposition of Reduced Dimension Hyperspectral Image

The application of anomaly detection has been given a special place among the different   processings of hyperspectral images. Nowadays, many of the methods only use background information to detect between anomaly pixels and background. Due to noise and the presence of anomaly pixels in the background, the assumption of the specific statistical distribution of the background, as well as the correlation between bands of hyperspectral images, leads to increase false alarms and the limitation of the presented methods in detecting anomalies. The purpose of this paper is to propose a new method for detecting anomalies with the ability to remove the limitations in background space. In the proposed method, first, the Fast Fourier Transform (FFT) is applied on the image as a preprocess of anomaly detection algorithms. Using this linear dimension reduction technique, in addition to improving the performance of the detection algorithm, can  significantly reduce the calculation. Then, by decomposition of reduced dimension hyperspectral image to the low-rank background matrix and the anomaly sparse matrix, in addition to separation of  the noise from the signals in the image, both the background and anomaly components can be used to extract information. In fact, by separating the component of the anomaly from the background, the effect of the existence of anomalous pixels in the background is reduced and only the low-rank matrix is used to extract information and statistical characteristics. Also, using the weighted average Mahalanobis distance based on the median criterion in the proposed decomposition method, we can allocate a background corresponding weight to each pixel and improve the anomalies detection results. The implementation of the proposed algorithm on the Pavia Hyperspectral Image and comparing its results with other common methods showed better performance of the proposed technique in detecting anomaly pixels from the background space.