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  • 1.
    Wang, Jianfeng
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Enhanced block sparse signal recovery and bayesian hierarchical models with applications2019Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    This thesis is carried out within two projects ‘Statistical modelling and intelligentdata sampling in Magnetic resonance imaging (MRI) and positron-emission tomography(PET) measurements for cancer therapy assessment’ and ‘WindCoE -Nordic Wind Energy Center’ during my PhD study. It mainly focuses on applicationsof Bayesian hierarchical models (BHMs) and theoretical developments ofcompressive sensing (CS). Under the first project, Paper I improves the quantityestimation of MRI parametric imaging by utilizing inherent dependent structure inthe image through BHMs; Paper III constructs a theoretically unbiased and asymptoticallynormal estimator of sparsity of a sparsified MR image by using a BHM;Paper IV extends block sparsity estimation from real-valued signal recovery tocomplex-valued signal recovery. It also demonstrates the importance of accuratelyestimating the block sparsity through a sensitivity analysis; Paper V proposes anew measure, i.e. q-ratio block constrained minimal singular value, of measurementmatrix for block sparse signal recovery. An algorithm for computing thisnew measure is also presented. In the second project, Paper II estimates the uncertaintyof Weather Research and Forecasting (WRF) model’s daily-mean 2-metertemperature in a cold region by using a BHM. It is a computationally cheaper andfaster alternative to traditional ensemble approach. In summary, this thesis makessignificant contributions in improving and optimizing the estimation proceduresof parameters of interest in MRI and WRF in practice, and developing the novelestimators and measure under the framework of CS in theory.

  • 2.
    Wang, Jianfeng
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    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 universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    A Hybrid Statistical-Dynamical Downscaling of Air Temperature over Scandinavia using the WRF model2020Ingår i: Advances in Atmospheric Sciences, ISSN 0256-1530, E-ISSN 1861-9533, Vol. 37, s. 57-74Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    An accurate simulation of air temperature at local-scales is crucial for the vast majority of weather and climate applications. In this work, a hybrid statistical-dynamical downscaling method and a high-resolution dynamical-only downscaling method are applied to daily mean, minimum and maximum air temperatures to investigate the quality of local scale estimates produced by downscaling. These two downscaling approaches are evaluated using station observation data obtained from the Finnish Meteorological Institute (FMI) over a near-coastal region of western Finland. The dynamical downscaling is performed with the Weather Research and Forecasting (WRF) model, and the statistical downscaling method implemented is the Cumulative Distribution Function-transform (CDF-t). The CDF-t is trained using 20-years of WRF-downscaled Climate Forecast System Reanalysis (CFSR) data over the region at 3 km spatial resolution for the central month of each season. The performance of the two methods is assessed qualitatively, by inspection of quantile-quantile (Q-Q) plots, and quantitatively, through the Cramer-von Mises (CvM), mean absolute error (MAE), and root-mean-square Error (RMSE) diagnostics. The hybrid approach is found to provide significantly more skillful forecasts of the observed daily mean and maximum air temperatures than those of the dynamical-only downscaling (for all seasons). The hybrid method proved to be less computationally expensive, and also to give more skillful temperature forecasts (at least for the Finnish near-coastal region).

  • 3.
    Wang, Jianfeng
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    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 universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Weather Simulation Uncertainty Estimation using Bayesian Hierarchical Model2019Ingår i: Journal of Applied Meteorology and Climatology, ISSN 1558-8424, E-ISSN 1558-8432, Vol. 58, nr 3, s. 585-603Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

  • 4.
    wang, jianfeng
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Garpebring, Anders
    Umeå universitet, Medicinska fakulteten, Institutionen för strålningsvetenskaper, Radiofysik.
    Brynolfsson, Patrik
    Umeå universitet, Medicinska fakulteten, Institutionen för strålningsvetenskaper, Radiofysik.
    Liu, Xijia
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Yu, Jun
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Contrast Agent Quantification by Using Spatial Information in Dynamic Contrast Enhanced MRIManuskript (preprint) (Övrigt vetenskapligt)
  • 5.
    Wang, Jianfeng
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Garpebring, Anders
    Umeå universitet, Medicinska fakulteten, Institutionen för strålningsvetenskaper.
    Brynolfsson, Patrik
    Umeå universitet, Medicinska fakulteten, Institutionen för strålningsvetenskaper, Radiofysik.
    Liu, Xijia
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Yu, Jun
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Contrast agent quantification by using spatial information in dynamic contrast enhanced MRI2016Manuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    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.

  • 6.
    Wang, Jianfeng
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Garpebring, Anders
    Umeå universitet, Medicinska fakulteten, Institutionen för strålningsvetenskaper.
    Brynolfsson, Patrik
    Umeå universitet, Medicinska fakulteten, Institutionen för strålningsvetenskaper.
    Yu, Jun
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Combining phase and magnitude information for contrast agent quantification in dynamic contrast-enhanced MRI using Bayesian hierarchical model2016Ingår i: Proceedings of the 8th International Workshop on Spatio-Temporal Modelling, 2016, s. 217-217Konferensbidrag (Övrigt vetenskapligt)
  • 7.
    Wang, Jianfeng
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Yu, Jun
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Sparsity Estimation of MR images in Compressive Sensing2017Konferensbidrag (Övrigt vetenskapligt)
  • 8.
    Wang, Jianfeng
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Zhou, Zhiyong
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Garpebring, Anders
    Umeå universitet, Medicinska fakulteten, Institutionen för strålningsvetenskaper.
    Yu, Jun
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Bayesian sparsity estimation in compressive sensing with application to MR images2019Ingår i: Communications in Statistics: Case Studies, Data Analysis and Applications, ISSN 2373-7484, Vol. 5, nr 4, s. 415-431Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The theory of compressive sensing (CS) asserts that an unknownsignal x ∈ CN can be 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. In the simulation study and real data study, magnetic resonance image data is used as input signal, which becomes sparse after sparsified transformation. The results from the simulation study confirm the theoretical properties of the estimator. In practice, the estimate from a real MR image can be used for recovering future MR images under the framework of CS if they are believed to have the same sparsity level after sparsification.

  • 9.
    Wang, Jianfeng
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Zhou, Zhiyong
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Garpebring, Anders
    Umeå universitet, Medicinska fakulteten, Institutionen för strålningsvetenskaper.
    Yu, Jun
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Sparsity estimation in compressive sensing with application to MR images2017Manuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    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.

  • 10.
    Wang, Jianfeng
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Zhou, Zhiyong
    Department of Statistics, Zhejiang University City College, China.
    Yu, Jun
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Error bounds of block sparse signal recovery based on q-ratio block constrained minimal singular values2019Ingår i: EURASIP Journal on Advances in Signal Processing, ISSN 1687-6172, E-ISSN 1687-6180, Vol. 2019, artikel-id 57Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we introduce the q-ratio block constrained minimal singular values (BCMSV) as a new measure of measurement matrix in compressive sensing of block sparse/compressive signals and present an algorithm for computing this new measure. Both the mixed ℓ2/ℓq and the mixed ℓ2/ℓ1 norms of the reconstruction errors for stable and robust recovery using block basis pursuit (BBP), the block Dantzig selector (BDS), and the group lasso in terms of the q-ratio BCMSV are investigated. We establish a sufficient condition based on the q-ratio block sparsity for the exact recovery from the noise-free BBP and developed a convex-concave procedure to solve the corresponding non-convex problem in the condition. Furthermore, we prove that for sub-Gaussian random matrices, the q-ratio BCMSV is bounded away from zero with high probability when the number of measurements is reasonably large. Numerical experiments are implemented to illustrate the theoretical results. In addition, we demonstrate that the q-ratio BCMSV-based error bounds are tighter than the block-restricted isotropic constant-based bounds.

  • 11.
    Wang, Jianfeng
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Zhou, Zhiyong
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. Department of Statistics, Zhejiang University City College, China.
    Yu, Jun
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Statistical inference for block sparsity of complex signals2019Manuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    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.

  • 12.
    Wang, Jianfeng
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Zhou, Zhiyong
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. Department of Statistics, Zhejiang University City College, China.
    Yu, Jun
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Statistical inference for block sparsity of complex-valued signals2020Ingår i: IET Signal Processing, ISSN 1751-9675, E-ISSN 1751-9683Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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 be estimated. 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 research that has been done for complex-valued signals. In this study, we propose a 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 through a sensitivity analysis.

1 - 12 av 12
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