A framework for dictionary learning based hyperspectral pixel classification

Abstract

This paper explores the utility of using dictionary learning as a preprocessing stage in the data reduction of hyperspectral data for the express purpose of improving detection and classification of materials. This paper sets up the general framework, and discusses some of the preliminary research from pairing a random forest classifier with dictionary learning. I. HYPERSPECTRAL DATAHyperspectral imaging (HSI) is the process of measuring or collecting an image across hundreds of spectral bands. This high spectral sample density warrants calling this a spectrum. Because of the nature of the sensor, HSI data forms a cube with the normal spatial dimensions and a third, spectral dimension. An example that demonstrates the idea of an HSI cube is in Fig 1.Fig. 1. A representation of a hyperspectral cube, illustrating both the spatial dimensions and the spectral dimension.The high spectral content of each pixel in an HSI cube can provide sufficient information to be able to classify materials based on their spectral signatures. Because of This work was supported by the Department of Energy under Grant No. this, it is used in many different fields including atmospheric sciences, geological surveys, medical imaging, and defense efforts. II. LINEAR MIXING MODELHSI pixels are commonly modeled using a linear mixing model, that is, each measured pixel x is a linear combination of some spectra from the constituent materials that are present in that pixel. Mathematically, this iswhere n is an AWGN noise vector, M is made up of spectral signatures of materials, and a provides the amounts corresponding to the contribution of each material to the pixel x. This linear mixing model is almost universally used in unmixing hyperspectral data. As an example of where the linearity is discussed in detail see [1] and references therein. III. PHYSICAL REALITIESGiven high enough spatial resolution, the assumption can be made that each pixel is a linear combination of only a few materials. For example, if each pixel corresponds to a 30 meter square on the ground, then there is the possibility of numerous different materials; whereas with a ground resolution of 1 meter then there are most likely only a few materials comprising a single pixel. If, in conjunction with high resolution, the given library M of spectra contains a large number of materials, probably more than would normally be present in any given scene, then the a in the linear mixing model is most likely very sparse, usually with only a few components that are nonzero. Thus it can be assumed that x = k a k m k , k ∈ K = {i|a i = 0}, |K| dim(a).