32.3 Linear Spectral Random Mixture Analysis for MRI

Recall that (32.1) is essentially a deterministic model, which assumes that signal sources img used for mixing are deterministic sources and the abundance fractions img are unknown constants and need to be estimated by solving unconstrained or constrained optimization problems. The OSP and FCLS developed in Section 32.2.1 provide unconstrained and constrained solutions, respectively.

In this section, we look into an alternative to the linear mixing model used in (32.1) in a very different way. In particular, we assume that the signal sources img in (32.1) are no longer deterministic sources, but rather random sources. More specifically, the signal sources img are considered as mutual statistically independent random processes. Given the nature of nonstationarity present in MR images, this assumption seems reasonable. On the other hand, two signal sources, which are considered to be distinct, are supposed to be uncorrelated in some sense. Mutual statistical independency provides, a good criterion to define distinct signal sources. With these assumptions ...

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