Symmetrized regression for hyperspectral background estimation

Abstract

We can improve the detection of targets and anomalies in a cluttered background by more effectively estimating that background. With a good estimate of what the target-free radiance or reflectance ought to be at a pixel, we have a point of comparison with what the measured value of that pixel actually happens to be. It is common to make this estimate using the mean of pixels in an annulus around the pixel of interest. But there is more information in the annulus than this mean value, and one can derive more general estimators than just the mean. The derivation pursued here is based on multivariate regression of the central pixel against the pixels in the surrounding annulus. This can be done on a band-by-band basis, or with multiple bands simultaneously.For overhead remote sensing imagery with square pixels, there is a natural eight-fold symmetry in the surrounding annulus, corresponding to reflection and right angle rotation. We can use this symmetry to impose constraints on the estimator function, and we can use these constraints to reduce the number or regressor variables in the problem. This paper investigates the utility of regression generally -and a variety of different symmetric regression schemes particularly -for hyperspectral background estimation in the context of generic target detection.

Graph-based and statistical approaches for detecting spectrally variable target materials

“…[15][16][17] The residual technique uses an annulus-based approach to obtain a "background-less" estimation of each pixel, and has shown success in hyperspectral anomaly detection. [18][19][20] These are described in more detail below, and illustrations are given in Figure 1.…”

“…[30][31][32][33][34] The idea of local means was extended to include more general local estimators based on functions of the pixels in the annulus. [18][19][20]35 background pixels in image subpixel target in image …”

Background estimation in multispectral imagery

“…In this scheme, each f d function is separately fit to the d'th band (another option is to constrain all f d functions to be the same). The most natural way to do this is to use the spectral bands, but it has been found empirically that employing principal component bands generally leads to better performance [15]. In addition to these spectral constraints, spatial constraints based on symmetry considerations have also been considered [15].…”

“…Most practical efforts to estimate f (x) for multispectral images have been limited to linear functions, and these have been found to be more effective than local means [14][15][16][17]. Estimates of the regression function f (x) can in principle call on all of the tools of machine learning, and there is every reason to believe that nonlinear f (x) can be more effective still.…”

“…Despite the long tradition of using a global mean in target detection, local background estimation was shown to be useful for small targets [11][12][13], and more recently, a learning-based framework was introduced [14][15][16][17]. Here, the pixel of interest is estimated by a general function (not just the mean) of the pixels in the annulus.…”