Analytical Comparison of the Matched Filter and Orthogonal Subspace Projection Detectors for Hyperspectral Images

In this paper, we perform an analytical comparison of two well-known detectors-the matched filter detector (MFD) and the orthogonal subspace projection (OSP) detector for the subpixel target detection in hyperspectral images under the assumption of the linear mixing model. The OSP detector (equivalent to the least-squares estimator) is a popular detector utilizing background signature information. On the other hand, the MFD is intended for a model without background information, and it is often used for its simplicity. The OSP detector seems to be more reliable because it removes the interference of background signatures. However, it has been demonstrated in the literature that sometimes the MFD can be more powerful. In this paper, we show an innovative approach to the evaluation of the detectors' performance. We prove the analytical results explaining the relationship between the two detectors beyond the anecdotal evidence from specific hyperspectral images or simulations. We also give some guidelines on when the MFD may be more beneficial than the OSP and when the OSP is better because of being more robust against a wide range of conditions. A major contribution of this paper is a development of a new approach to the comparison of detectors.