Diffusion Tensor Imaging and Deconvolution on Spaces of Positive Definite Symmetric Matrices
نویسنده
چکیده
Diffusion tensor imaging can be studied as a deconvolution density estimation problem on the space of positive definite symmetric matrices. We develop a nonparametric estimator for the common density function of a random sample of positive definite matrices. Our estimator is based on the Helgason-Fourier transform and its inversion, the natural tools for analysis of compositions of random positive definite matrices. Under smoothness conditions on the density of the intrinsic error in the random sample, we derive bounds on the rates of convergence of our nonparametric estimator to the true density.
منابع مشابه
Deconvolution Density Estimation on Spaces of Positive Definite Symmetric Matrices
Motivated by applications in microwave engineering and diffusion tensor imaging, we study the problem of deconvolution density estimation on the space of positive definite symmetric matrices. We develop a nonparametric estimator for the density function of a random sample of positive definite matrices. Our estimator is based on the Helgason-Fourier transform and its inversion, the natural tools...
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