Locally Adaptive Constrained Energy Minimization for Aviris Images

The Constrained Energy Minimization (CEM) technique (Harsanyi, 1993) has become quite popular in recent years as a means for constructing a linear operator to perform matched filtering of hyperspectral images. The CEM algorithm tries to maximize the response of the target spectral signature while suppressing the response of the unknown background signatures. This technique has its roots in signal processing theory and has long been used in electrical engineering applications. The CEM technique constructs an optimal linear operator that, when applied to a hyperspectral image, produces an abundance map for the every image pixel vector. The algorithm uses an estimate of the sample correlation matrix as a basis for determining the unknown background signatures and is computationally efficient. Application of the algorithm to a hyperspectral image usually provides strong suppression of the undesired signatures and enhances the contrast between target spectra and the background. These properties make the CEM algorithm a very popular processing technique as well as a common component of more complicated algorithms. However, the CEM approach has a number of significant shortcomings. It doesn’t perform well in the presence of low probability background signatures, and an abundance image may contain a significant amount of noise and false alarms that make detection of small targets difficult. The standard CEM algorithm uses a single overall correlation matrix as a description of the undesired background signatures. Consequently, the performance of the algorithm is directly related to the complexity and diversity of the hyperspectral scene. Some of the existing modifications of the CEM technique try to improve the performance of the method by introducing spectral variability to the traditional single spectrum design (Farrand and Harsanyi, 1997; Boardman, 1998).