A study between orthogonal subspace projection and generalized likelihood ratio test in hyperspectral image analysis

Orthogonal subspace projection (OSP) and generalized likelihood ratio test (GLRT) have shown success in hyperspectral image classification. The OSP is derived by maximizing signal-to-noise ratio (SNR) resulting from a linear mixture model in which the noise is assumed to be white. On the other hand, the GLRT is formulated based on a signal detection model that can be described by a binary hypothesis testing problem. In order for the GLRT to derive an analytical form, the noise in the signal detection model is generally assumed to be white Gaussian noise. However, Gaussianity is generally not true in remotely sensed imagery. Interestingly, such assumption has not been investigated. This paper presents a comparative study between OSP and GLRT based on their assumptions. In particular, a detailed analysis of assumptions made on these two approaches is conducted through a series of computer simulations. Experimental results show that the OSP does not depend on Gaussian noise. By the contrast, the GLRT is affected by the Gaussian noise assumption. If it is violated, its performance is degraded.