3 Matching Results

Search Results

Advanced search parameters have been applied.

Tradeoffs between measurement residual and reconstruction error in inverse problems with prior information

Description: In many inverse problems with prior information, the measurement residual and the reconstruction error are two natural metrics for reconstruction quality, where the measurement residual is defined as the weighted sum of the squared differences between the data actually measured and the data predicted by the reconstructed model, and the reconstruction error is defined as the sum of the squared differences between the reconstruction and the truth, averaged over some a priori probability space of possible solutions. A reconstruction method that minimizes only one of these cost functions may produce unacceptable results on the other. This paper develops reconstruction methods that control both residual and error, achieving the minimum residual for any fixed error or vice versa. These jointly optimal estimators can be obtained by minimizing a weighted sum of the residual and the error; the weights are determined by the slope of the tradeoff curve at the desired point and may be determined iteratively. These results generalize to other cost functions, provided that the cost functions are quadratic and have unique minimizers; some results are obtained under the weaker assumption that the cost functions are convex. This paper applies these results to a model problem from biomagnetic source imaging and exhibits the tradeoff curve for this problem.
Date: June 1, 1995
Creator: Hughett, P.
Partner: UNT Libraries Government Documents Department

Algorithms for biomagnetic source imaging with prior anatomical and physiological information

Description: This dissertation derives a new method for estimating current source amplitudes in the brain and heart from external magnetic field measurements and prior knowledge about the probable source positions and amplitudes. The minimum mean square error estimator for the linear inverse problem with statistical prior information was derived and is called the optimal constrained linear inverse method (OCLIM). OCLIM includes as special cases the Shim-Cho weighted pseudoinverse and Wiener estimators but allows more general priors and thus reduces the reconstruction error. Efficient algorithms were developed to compute the OCLIM estimate for instantaneous or time series data. The method was tested in a simulated neuromagnetic imaging problem with five simultaneously active sources on a grid of 387 possible source locations; all five sources were resolved, even though the true sources were not exactly at the modeled source positions and the true source statistics differed from the assumed statistics.
Date: December 1995
Creator: Hughett, P. W.
Partner: UNT Libraries Government Documents Department

A comparison of vector and radial magnetometer arrays for whole-head magnetoencephalography

Description: The number of detectors in magnetometer arrays for magnetoencephalography (MEG) has been steadily increasing, with systems containing or more detectors now possible. It is of considerable interest to know how best to configure such a large array. In particular, is it useful to measure all three components of the magnetic field, rather than just the radial component? This paper compares the information content provided by three different magnetometer arrays for whole-head measurements, using a definition of information content developed by Kemppainen and Ilmoniemi.
Date: February 1, 1996
Creator: Hughett, P. & Miyauchi, S.
Partner: UNT Libraries Government Documents Department