Automatic 4-D Registration in Dynamic MR Renography Based on Over-complete Dyadic Wavelet and Fourier Transforms

Dynamic contrast-enhanced 4-D MR renography has the potential for broad clinical applications, but suffers from respiratory motion that limits analysis and interpretation. Since each examination yields at least over 10-20 serial 3-D images of the abdomen, manual registration is prohibitively labor-intensive. Besides in-plane motion and translation, out-of-plane motion and rotation are observed in the image series. In this paper, a novel robust and automated technique for removing out-of-plane translation and rotation with sub-voxel accuracy in 4-D dynamic MR images is presented. The method was evaluated on simulated motion data derived directly from a clinical patient's data. The method was also tested on 24 clinical patient kidney data sets. Registration results were compared with a mutual information method, in which differences between manually co-registered time-intensity curves and tested time-intensity curves were compared. Evaluation results showed that our method agreed well with these ground truth data

On the ultimate convergence rates for isotropic algorithms and the best choices among various forms of isotropy

In this paper, we show universal lower bounds for isotropic algorithms, that hold for any algorithm such that each new point is the sum of one already visited p oint plus one random isotropic direction multiplied by any step size (whenever the step size is chosen by an oracle with arbitrarily high computational power). The bound is 1 − O(1/d) for the constant in the linear convergence (i.e. the constant C such that the distance to the optimum after n steps is upp er b ounded by C n ), as already seen for some families of evolution strategies in [19, 12], in contrast with 1 − O(1) for the reverse case of a random step size and a direction chosen by an oracle with arbitrary high computational power. We then recall that isotropy does not uniquely determine the distribution of a sample on the sphere and show that the convergence rate in isotropic algorithms is improved by using stratified or antithetic isotropy instead of naive isotropy. We show at the end of the pap er that b eyond the mathematical proof, the result holds on exp eriments. We conclude that one should use antithetic-isotropy or stratified-isotropy, and never standard-isotropy

Finding Building Blocks through Eigenstructure Adaptation

A fundamental aspect of many evolutionary approaches to synthesis of complex systems is the need to compose atomic elements into useful higher-level building blocks. However, the ability of genetic algorithms to promote useful building blocks is based critically on genetic linkage – the assumption that functionally related alleles are also arranged compactly on the genome. In many practical problems, linkage is not known a priori or may change dynamically. Here we propose that the problems ’ Hessian matrix reveals this linkage, and that an eigenstructure analysis of the Hessian provides a transformation of the problem to a space where first-order genetic linkage is optimal. Genetic algorithms that dynamically transform the problem space can operate much more efficiently. We demonstrate the proposed approach on a real-valued adaptation of Kaufmann’s NK landscapes