Estimation of conditional distribution functions from data with additional errors applied to shape optimization

We study the problem of estimating conditional distribution functions from data containing additional errors. The only assumption on these errors is that a weighted sum of the absolute errors tends to zero with probability one for sample size tending to infinity. We prove sufficient conditions on the weights (e.g. fulfilled by kernel weights) of a local averaging estimate of the codf, based on data with errors, which ensure strong pointwise consistency. We show that two of the three sufficient conditions on the weights and a weaker version of the third one are also necessary for the spc. We also give sufficient conditions on the weights, which ensure a certain rate of convergence. As an application we estimate the codf of the number of cycles until failure based on data from experimental fatigue tests and use it as objective function in a shape optimization of a component.

Application of an Improved Seeds Local Averaging Algorithm in X-ray Spectrum

As an element content analysis technology, X-ray fluorescence spectrometry can be used for quantitative or semiquantitative analysis of the element content in the sample, which is of great significance for mineral census and spent fuel reprocessing. Due to the limitation of the inherent energy resolution of the detector itself, the accuracy of X-ray fluorescence analysis is difficult to be greatly improved. In some applications, even if the semiconductor detector with the best energy resolution is used, the characteristic peaks of different elements cannot be completely separated. Therefore, greatly improving the energy resolution of the detection system is a hot issue in the existing research field. To solve these problems, this paper analyzes the advantages and disadvantages of the traditional MCA (multichannel analyzer) and SLA (seeds local averaging) algorithm and proposes an ISLA (improved seeds local averaging) algorithm based on mathematical statistics. In the section of theoretical derivation, the principle of ISLA algorithm is described, whose theoretical characteristics and spectral results with different parameters are derived and simulated. In the application effect evaluation, the spectrum obtained by each method is analyzed in detail. Simulation and experimental results show that the spectrum obtained by SLA algorithm has a smaller full width at half maximum than that obtained by MCA, but the seed average process in SLA algorithm also reduces its counting rate. The optimized ISLA algorithm can not only effectively reduce the full width at half maximum of the spectral line and sharpen the spectrum peak but also compensate for the loss of the count rate of SLA algorithm.

Efficient and Robust Non-Local Means Denoising Methods for Biomedical Images

Denoising is an important step to improve image quality and to increase the performance of image analysis. However, conventional partial differential equation based image denoising methods, especially total variation functional minimization techniques, do not work very well on biomedical images such as magnetic resonance images (MRI), ultrasound, and X-ray images. These images present small structures with signals barely detectable above the noise level which involve more complex noise and unclear edges. The recently developed non-local means (NLM) filtering method can treat these types of images better. The standard NLM filter uses the weighted averages of similar patches present in the image. Since the NLM filter is anon-local averaging method, it is very accurate in removing noise but has computational complexity. We develop efficient and optimized NLM based methods and their associate numerical algorithms. The new methods are still accurate enough and moreeffi-cient than the original NLM filter. Numerical results show that the new methods compare favorably to the conventional denoising methods.

Atlas-based classification algorithms for identification of informative brain regions in fMRI data

Multi-voxel pattern analysis (MVPA) has been successfully applied to neuroimaging data due to its larger sensitivity compared to univariate traditional techniques. Searchlight is the most widely employed approach to assign functional value to different regions of the brain. However, its performance depends on the size of the sphere, which can overestimate the region of activation when a large sphere size is employedIn the current study, we examined the validity of two different alternatives to Searchlight: an atlas-based local averaging method (ABLA, Schrouff et al., 2013a) and a Multi-Kernel Learning (MKL, Rakotomamonjy et al., 2008) approach, in a scenario where the goal is to find the informative brain regions that support certain mental operations. These methods employ weights to measure the informativeness of a brain region and highly reduce the large computational cost that Searchlight entails. We evaluated their performance in two different scenarios where the differential BOLD activation between experimental conditions was large vs. small, and employed nine different atlases to assess the influence of diverse brain parcellations.Results show that both methods were able to localize informative regions when differences between conditions were large, demonstrating a large sensitivity and stability in the identification of regions across atlases. Moreover, the sign of the weights reported by these methods provided the directionality of univariate approaches. However, when differences were small, only ABLA localized informative regions. Thus, our results show that atlas-based methods are useful alternatives to Searchlight, but that the nature of the classification to perform should be taken into account when choosing the specific method to implement.