Physics – Medical Physics
Scientific paper
1999-11-10
Physics
Medical Physics
10 pages, 6 figures, submitted to Inverse Problems
Scientific paper
In an inverse problem, such as the determination of brain activity given magnetic field measurements outside the head, the main quantity of interest is often the power associated with a source. The `standard' way to determine this has been to find the best linear estimate of the source and calculate the power associated with this. This paper proposes an alternative method and then relationship to this previous method of estimation is explored both algebraically and by numerical simulation. In abstract terms the problem can be stated as follows. Let H be a Hilbert space with inner product <, >. Let L be a linear map: H->R^n. Suppose that we are a given data vector b in R^n such that b=Lx+e where e is a vector of random variables with zero mean and given covariance matrix that represents measurement errors. The problem that is addressed in this paper is to estimate
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