Spatial-temporal Source Reconstruction for Magnetoencephalography

Magnetoencephalography (MEG) is a new non-invasive technique for the
functional imaging of the human brain. It has been widely used in both
research and clinical applications, for it has several superior properties,
including a high-temporal resolution with no interference from the bone
or the head-like fluid to the signal spatial transformation.

In this thesis, we aim to develop a framework for MEG spatial-temporal
current course reconstruction by introducing classical methods from the
pattern recognition theory into medical imaging. These applications provide
a new angle for research in MEG source reconstruction with the solution
for source reconstruction at a single point, and improvements of the
reconstruction on spatially and temporally. The whole thesis is based on
three topics, which are designed to be parts of an integrated reconstruction
process, and each of them are interrelated, rather than independent from
each other.

We firstly introduce the source reconstructionmethod at a single time point
using the basis function extraction. In light of the assumption that the
Laplacian eigenvectors of mesh can be the analogous to the basis functions
that represent the cortex mesh; we build a new model to describe the
current source that is distributed on each mesh vertex. This model consists
of analogous basis functions and unknown weighted coefficients. In terms
of experiment results, this algorithm shows good reconstructed property
to the single stimulus, as well as the supercial stimulus on the cortical
surface.

Secondly, with respect to the spatial reconstructed sources by basis function
method from the last topic, we build a new solution for improving
the spatial-resolution of MEG source reconstruction at a single time point by introducing a classical method ( the Bayesian super-resolution
method) from the pattern recognition theory. Although the approach is designed based on the reconstruction from basis functions, it is also feasible
for other spatial reconstruction methods to improve the spatial-resolution.
From the numerical experiment results, it is apparent that the spatial resolution has been effectively improved.

Then, the MEG measurement system in the temporal field is assumed to
be a linear dynamic system where the classical methods, Kalman filter and
Kalman smoother, are applied as the solution for the estimation of source
in time course. The Kalman filter is used to estimate the dynamic state
while the Kalman smoother is applied for correcting the source distribution
of the hidden state with the EMalgorithm. This approach shows superior
performance to solve the inverse problem. It extends the improvement
in source reconstruction using the temporal field.

We construct the synthetic data as well as apply the realMEG data throughout
all the experimental test of my work.

In summary, this thesis builds three algorithms, which aim to reconstruct
the MEG source distribution on spatial and temporal field respectively
aided by methods from pattern recognition. This work provides a new
angle of using the pattern recognition theory for MEG source reconstruction.
Meanwhile, we also explore a new direction for applying the theory
of pattern recognition. This work not only provides a good integration
between these two fields, but also encourage future interactions.