Fiber Orientation Distribution Estimation Via Gauge Duality

In medical engineering,the technology of magnetic resonance imaging has been ma-ture early and used widely.Especially in the area of exploring cerebral nerve fibers.The estimation of fiber orientation distribution is the key of studying fiber direction.In my master thesis,we construct a new spherical deconvolution model to study the question by a convex positive semi-definite optimization.The purpose is to find a probability density funct.ion of fiber orientation which satisfies the statistical significance.We choose squares-of-sum polynomial with a linear constraint of integration into one to approximate it.For convenient calculation,we study the gauge duality of the new spherical deconvolution mod-el,and solve the gauge program with alternating direction methods.In the last,we get some pictures by numerical experiments with matlab and noiseless signals which simulates the real brain fiber distribution,including least squares and our new gauge dual program.Obviously,the effect of numerical experiment shows the gauge duality is better than least squares which shows the effectiveness of the new model.