Nonparametric weighted feature extraction for noise whitening least squares

The Least Square (LS) approach is one of the most widely used algorithms for target detection in remote sensing images. It has been proven mathematically that the Noise Whitened Least Square (NWLS) can outperform the original version by making the noise distribution independent and identical distributed (i.i.d.). But in order to have good results, the estimation of the noise covariance matrix is very important and still remains a great challenge. Many estimation methods have been proposed in the past. The first type of methods assumes that the signal between neighbor pixels should be similar, so that the difference between neighborhood pixels or the high-frequency signals can be used to represent noise. These includes spatial and frequency domain high-pass filter, neighborhood pixel subtraction. The more practical method is based on the training samples and calculates the covariance matrix between each training sample and its class mean as the noise distribution, which is the within-class scatter matrix in Fisher's Linear Discriminant Analysis. But it is usually not easy to collect enough training samples to yield full rank covariance matrix. In this paper, we adopt the Nonparametric Weighted Feature Extraction (NWFE) to overcome the rank problem and it is also suitable to model the non-Gaussian noise. We have also compared the results with SPOT-5 image scene.