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Hyperspectral data unmixing and target detection and classification are two important areas of hyperspectral data processing. This paper provides a seminal view on the relevance of four most widely used models in hyperspectral data unmixing. We describe the algorithms in summary and discuss the connections and differences of these four models. Unconstrained least squares unmixing (ULSU) is an earlier approach to estimate abundance fractions based on linear mixing models. Orthogonal subspace projection (OSP), Mixture-Tuned Matched Filtering Approach (MTMF) and Matched Filter with False Alarm Mitigation (MF-FAM) are developed for target detection at first but soon show their potential in hyperspectral data unmixing. Theoretically, LSMA without any constraints on the abundance fractions can estimate all abundance fractions for one time with the prior knowledge of entire signatures. OSP is able to gain abundance fractions and detect constituent materials for each pixel on the premise of the prior knowledge of desired and undesired signature. Each operation obtains each pixel result. By comparing, we find that an abundance-unconstrained LSMA has the same classification feature as OSP but with an extra constant. According to the first part MF of MTMF, the linear optimal signal detector of OSP is a background rejecter followed by a matched filter with the matched signal when the constant is equal to one. Both MTMF and MF-FAM firstly use matched filter to get MF scores. MTMF decomposes into two parts, the first part corresponds to MF, while the second part resembles MT. Both parts are based on projection. Versus the morphing space, the first part MF of MTMF can be taken as projection on the vertical axis, and MT are projected to the horizontal axis. MF-FAM also makes a vertical projection at first to obtain MF values, but it acquires false alarm mitigation by using probability density function of pixels from a statistical perspective.
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