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1.

Wang, Jianfeng

et al.

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

Fonseca, Ricardo M.

Group of Atmospheric Science, Division of Space Technology, Department of Computer Science, Electrical and Space Engineering, Luleå University of Technology.

Rutledge, Kendall

Novia University of Applied Sciences, Vaasa, Finland.

Martin-Torres, Javier

Group of Atmospheric Science, Division of Space Technology, Department of Computer Science, Electrical and Space Engineering, Luleå University of Technology.

Yu, Jun

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

Estimates of the uncertainty of model output fields (e.g. 2-meter temperature, surface radiation fluxes or wind speed) are of great value to the weather and climate communities. The traditional approach for the uncertainty estimation is to conduct an ensemble of simulations where the model configuration is perturbed, and/or different models are considered. This procedure is very computationally expensive and may not be feasible in particular for higher resolution experiments. In this paper a new method based on Bayesian Hierarchical Models (BHM) that requires just one model run is proposed. It is applied to the Weather Research and Forecasting (WRF) model’s 2-meter temperature in the Botnia-Atlantica region in Scandinavia for a 10-day period in the winter and summer seasons. For both seasons, the estimated uncertainty using the BHM is found to be comparable to that obtained from an ensemble of experiments in which different Planetary Boundary Layer (PBL) schemes are employed. While WRF-BHM is not capable of generating the full set of products obtained from an ensemble of simulations, it can be used to extract commonly used diagnostics including the uncertainty estimation which is the focus of this work. The methodology proposed here is fully general and can easily be extended to any other output variable and numerical model.

The purpose of this study is to investigate a method, using simulations, toimprove contrast agent quantication in Dynamic Contrast Enhanced MRI.Bayesian hierarchical models (BHMs) are applied to smaller images such that spatial information can be incorporated. Then exploratory analysisis done for larger images by using maximum a posteriori (MAP).

For smaller images: the estimators of proposed BHMs show improvementsin terms of the root mean squared error compared to the estimators in existingmethod for a noise level equivalent of a 12-channel head coil at 3T. Moreover,Leroux model outperforms Besag models. For larger images: MAP estimatorsalso show improvements by assigning Leroux prior.

3.

wang, jianfeng

et al.

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

Garpebring, Anders

Umeå University, Faculty of Medicine, Department of Radiation Sciences, Radiation Physics.

Brynolfsson, Patrik

Umeå University, Faculty of Medicine, Department of Radiation Sciences, Radiation Physics.

Liu, Xijia

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

Yu, Jun

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

The theory of compressive sensing (CS) asserts that an unknown signal x in C^N canbe accurately recovered from m measurements with m << N provided that x is sparse. Most of the recovery algorithms need the sparsity s = ||x||_0 as an input. However,generally s is unknown, and directly estimating the sparsity has been an open problem.In this study, an estimator of sparsity is proposed by using Bayesian hierarchical model. Its statistical properties such as unbiasedness and asymptotic normality are proved. Inthe simulation study and real data study, magnetic resonance image data is used asinput signal, which becomes sparse after sparsified transformation. The results fromthe simulation study confirm the theoretical properties of the estimator. In practice, theestimate from a real MR image can be used for recovering future MR images under theframework of CS if they are believed to have the same sparsity level after sparsification.

7.

Wang, Jianfeng

et al.

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

Zhou, Zhiyong

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Department of Statistics, Zhejiang University City College, China.

Yu, Jun

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.

Block sparsity is an important parameter in many algorithms to successfully recover block sparse signals under the framework of compressive sensing. However, it is often unknown and needs to beestimated. Recently there emerges a few research work about how to estimate block sparsity of real-valued signals, while there is, to the best of our knowledge, no investigation that has been conductedfor complex-valued signals. In this paper, we propose a new method to estimate the block sparsity of complex-valued signal. Its statistical properties are obtained and verified by simulations. In addition,we demonstrate the importance of accurately estimating the block sparsity in signal recovery through asensitivity analysis.