Maximum likelihood estimation for rician distributed data in analytical q-ball imaging

Analytical q-ball imaging is widely used for reconstruction of orientation distribution function (ODF) using diffusion weighted MRI data. Estimating the spherical harmonic coefficients is a critical step in this method. Least squares (LS) is widely used for this purpose assuming the noise to be additive Gaussian. However, Rician noise is considered as a more appropriate model to describe noise in MR signal. Therefore, the current estimation techniques are valid only for high SNRs with Gaussian distribution approximating the Rician distribution. The aim of this study is to present an estimation approach considering the actual distribution of the data to provide reliable results particularly for the case of low SNR values. Maximum likelihood (ML) is investigated as a more effective estimation method. However, no closed form estimator is presented as the estimator becomes nonlinear for the noise assumption of the Rician distribution. Consequently, the results of LS estimator is used as an initial guess and the more refined answer is achieved using iterative numerical methods. According to the results, the ODFs reconstructed from low SNR data are in close agreement with ODFs reconstructed from high SNRs when Rician distribution is considered. Also, the error between the estimated and actual fiber orientations was compared using ML and LS estimator. In low SNRs, ML estimator achieves less error compared to the LS estimator.

Maximum-likelihood based estimation for Q-ball imaging using diffusion-weighted MRI data

Q-ball imaging has been presented to reconstruct diffusion orientation distribution function using diffusion weighted MRI. In this thesiis, we present a novel and robust approach to satisfy the smoothness constraint required in Q-ball imaging. Moreover, we developed an improved estimator based on the actual distribution of the MR data.

Harajuku : urban stage-set Q & A

Harajuku is arguably one of the most exciting and vibrant fashion precincts of Tokyo. Through a series of questions and answers, Harajuku Urban Stage-Set captures the urban character of the precinct and the complexity of that unique place

Editorial : Q & A John A. Endler

John A. Endler is a Professor of Sensory Ecology and Evolution at Deakin University and an Adjunct professor of Zoology at James Cook University, both in Australia. He regards himself as a 19th century natural historian who uses 21st century techniques to answer questions generated originally from field observations. His research is in the area of overlap among Evolutionary Biology, Sensory Ecology, Behavioural Ecology, Animal Behaviour, Neuroethology and Biophysics. He enjoys combining field work, field experiments, lab work, and theoretical methods as well as constructing electromechanical-optical equipment and software for himself and students.