Weighted Fourier Image Analysis and Modeling

A novel systematic framework of medical image analysis, weighted Fourier series (WFS) analysis is introduced. WFS is a combination of Fourier series and heat kernel smoothing. WFS effectively reduces the Gibbs phenomenon, improves the signal to noise ratio, and increases normality of the estimated errors in the WFS-based generalized linear models. In estimating the parameters of WFS, the least squares estimation of WFS has been widely used but it is computationally inefficient. To address the computational inefficiency in the least squares estimation, much faster but less accurate iterative residual fitting (IRF) method has been proposed. The proposed adaptive iterative regression (AIR) technique inherits the computational efficiency of IRF and improves accuracy of IRF. AIR partitions the function space into a set of subspaces, and performs an extra orthogonalization procedure to reduce the bias of IRF estimation. A complimentary tool, the fast weighted Fourier analysis method computes the coefficients of WFS efficiently and chooses the significant frequencies of WFS representations automatically. As a model selection tool, its accuracy is comparable with other model selection methods. Its computational efficiency outperforms other classic model selection methods. For robust and accurate curvature estimation, we propose a new curve curvature calculation method. This method is independent of parametrization so