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Open this publication in new window or tab >>A Hybrid Statistical-Dynamical Downscaling of Air Temperature over Scandinavia using the WRF model### Wang, Jianfeng

### Fonseca, Ricardo M.

### Rutledge, Kendall

### Martin-Torres, Javier

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); ### Yu, Jun

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt184_0_j_idt188_j_idt202",{id:"formSmash:j_idt184:0:j_idt188:j_idt202",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_j_idt202",onLabel:"Hide others...",offLabel:"Show others..."}); 2020 (English)In: Advances in Atmospheric Sciences, ISSN 0256-1530, E-ISSN 1861-9533, Vol. 37, p. 57-74Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Springer, 2020
##### Keywords

WRF, air temperature, CDF-t, hybrid statistical-dynamical downscaling, model evaluation, Scandinavian Peninsula.
##### National Category

Probability Theory and Statistics Meteorology and Atmospheric Sciences
##### Research subject

Mathematical Statistics
##### Identifiers

urn:nbn:se:umu:diva-162956 (URN)10.1007/s00376-019-9091-0 (DOI)
#####

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##### Projects

WindCoE
Available from: 2019-09-03 Created: 2019-09-03 Last updated: 2020-01-07Bibliographically approved

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

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

Novia University of Applied Sciences, Vaasa, Finland.

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

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

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).

Open this publication in new window or tab >>Statistical inference for block sparsity of complex-valued signals### Wang, Jianfeng

### Zhou, Zhiyong

### Yu, Jun

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 2020 (English)In: IET Signal Processing, ISSN 1751-9675, E-ISSN 1751-9683Article in journal (Refereed) Accepted
##### Abstract [en]

##### Place, publisher, year, edition, pages

Institution of Engineering and Technology, 2020
##### Keywords

Block sparsity; Complex-valued signals; Multivariate isotropic symmetric alpha-stable distributions
##### National Category

Probability Theory and Statistics Signal Processing
##### Research subject

Mathematical Statistics
##### Identifiers

urn:nbn:se:umu:diva-168016 (URN)10.1049/iet-spr.2019.0200 (DOI)
#####

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Available from: 2020-02-10 Created: 2020-02-10 Last updated: 2020-02-18

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

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

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.

Open this publication in new window or tab >>A New Nonconvex Sparse Recovery Method for Compressive Sensing### Zhou, Zhiyong

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.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: Frontiers in Applied Mathematics and Statistics, ISSN 2297-4687, Vol. 5, p. 1-11, article id 14Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Frontiers Media S.A., 2019
##### Keywords

compressive sensing, nonconvex sparse recovery, iteratively reweighted least squares, difference of convex functions, q-ratio constrained minimal singular values
##### National Category

Signal Processing Mathematics
##### Research subject

Signal Processing; Mathematical Statistics
##### Identifiers

urn:nbn:se:umu:diva-157346 (URN)10.3389/fams.2019.00014 (DOI)
#####

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##### Funder

Swedish Research Council, 340-2013-5342
Available from: 2019-03-15 Created: 2019-03-15 Last updated: 2019-03-20Bibliographically approved

As an extension of the widely used ℓr-minimization with 0 < r ≤ 1, a new non-convex weighted ℓr − ℓ1 minimization method is proposed for compressive sensing. The theoretical recovery results based on restricted isometry property and q-ratio constrained minimal singular values are established. An algorithm that integrates the iteratively reweighted least squares algorithm and the difference of convex functions algorithmis given to approximately solve this non-convex problem. Numerical experiments are presented to illustrate our results.

Open this publication in new window or tab >>Adaptive algorithm for sparse signal recovery### Bayisa, Fekadu

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.### Cronie, Ottmar

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.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: Digital signal processing (Print), ISSN 1051-2004, E-ISSN 1095-4333, Vol. 87, p. 16p. 10-18Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Elsevier, 2019. p. 16
##### Keywords

sparsity, adaptive algorithm, sparse signal recovery, spike and slab priors
##### National Category

Probability Theory and Statistics Signal Processing Medical Image Processing
##### Research subject

Mathematical Statistics; Signal Processing
##### Identifiers

urn:nbn:se:umu:diva-146386 (URN)10.1016/j.dsp.2019.01.002 (DOI)000461266700002 ()2-s2.0-85060542792 (Scopus ID)
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##### Projects

Statistical modelling and intelligent data sampling in MRI and PET measurements for cancer therapy assessment
##### Funder

Swedish Research Council, 340-2013-534
##### Note

The development of compressive sensing in recent years has given much attention to sparse signal recovery. In sparse signal recovery, spike and slab priors are playing a key role in inducing sparsity. The use of such priors, however, results in non-convex and mixed integer programming problems. Most of the existing algorithms to solve non-convex and mixed integer programming problems involve either simplifying assumptions, relaxations or high computational expenses. In this paper, we propose a new adaptive alternating direction method of multipliers (AADMM) algorithm to directly solve the suggested non-convex and mixed integer programming problem. The algorithm is based on the one-to-one mapping property of the support and non-zero element of the signal. At each step of the algorithm, we update the support by either adding an index to it or removing an index from it and use the alternating direction method of multipliers to recover the signal corresponding to the updated support. Moreover, as opposed to the competing “adaptive sparsity matching pursuit” and “alternating direction method of multipliers” methods our algorithm can solve non-convex problems directly. Experiments on synthetic data and real-world images demonstrated that the proposed AADMM algorithm provides superior performance and is computationally cheaper than the recently developed iterative convex refinement (ICR) and adaptive matching pursuit (AMP) algorithms.

Originally included in thesis in manuscript form

Available from: 2018-04-07 Created: 2018-04-07 Last updated: 2019-04-04Bibliographically approvedOpen this publication in new window or tab >>Adaptive estimation for varying coefficient modelswith nonstationary covariates### Zhou, Zhiyong

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.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 48, no 16, p. 4034-4050Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Taylor & Francis, 2019
##### Keywords

Varying coefficient model, adaptive estimation, local linear fitting, non stationary covariates
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematical Statistics
##### Identifiers

urn:nbn:se:umu:diva-154754 (URN)10.1080/03610926.2018.1484483 (DOI)000473519800007 ()2-s2.0-85059303429 (Scopus ID)
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##### Funder

Swedish Research Council, 340-2013-534
Available from: 2018-12-30 Created: 2018-12-30 Last updated: 2019-08-06Bibliographically approved

In this paper, the adaptive estimation for varying coefficient models proposed by Chen, Wang, and Yao (2015) is extended to allowing for nonstationary covariates. The asymptotic properties of the estimator are obtained, showing different convergence rates for the integrated covariates and stationary covariates. The nonparametric estimator of the functional coefficient with integrated covariates has a faster convergence rate than the estimator with stationary covariates, and its asymptotic distribution is mixed normal. Moreover, the adaptive estimation is more efficient than the least square estimation for non normal errors. A simulation study is conducted to illustrate our theoretical results.

Open this publication in new window or tab >>An extended block restricted isometry property for sparse recovery with non-Gaussian noise### Leffler, Klara

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

### Yu, Jun

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: Journal of Computational Mathematics, ISSN 0254-9409, E-ISSN 1991-7139Article in journal (Refereed) Epub ahead of print
##### Abstract [en]

##### Place, publisher, year, edition, pages

Global Science Press, 2019
##### Keywords

Compressed sensing, block sparsity, partial support information, signal reconstruction, convex optimization
##### National Category

Signal Processing Probability Theory and Statistics Computational Mathematics
##### Research subject

Mathematical Statistics
##### Identifiers

urn:nbn:se:umu:diva-163366 (URN)10.4208/jcm.1905-m2018-0256 (DOI)
#####

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##### Funder

Swedish Research Council
Available from: 2019-09-17 Created: 2019-09-17 Last updated: 2019-11-19

Department of Statistics, Zhejiang University City College, China.

We study the recovery conditions of weighted mixed ℓ2/ℓp minimization for block sparse signal reconstruction from compressed measurements when partial block supportinformation is available. We show theoretically that the extended block restricted isometry property can ensure robust recovery when the data fidelity constraint is expressed in terms of an ℓq norm of the residual error, thus establishing a setting wherein we arenot restricted to Gaussian measurement noise. We illustrate the results with a series of numerical experiments.

Open this publication in new window or tab >>Bayesian sparsity estimation in compressive sensing with application to MR images### Wang, Jianfeng

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.### Garpebring, Anders

### Yu, Jun

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: Communications in Statistics: Case Studies, Data Analysis and Applications, ISSN 2373-7484, Vol. 5, no 4, p. 415-431Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Taylor & Francis Group, 2019
##### Keywords

Compressive sensing, sparsity, Bayesian hierarchical model, Matérn covariance, MRI
##### National Category

Probability Theory and Statistics Signal Processing Medical Image Processing
##### Research subject

Mathematical Statistics
##### Identifiers

urn:nbn:se:umu:diva-164952 (URN)10.1080/23737484.2019.1675557 (DOI)
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Available from: 2019-11-05 Created: 2019-11-05 Last updated: 2019-12-16Bibliographically approved

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

The theory of compressive sensing (CS) asserts that an unknownsignal **x** ∈ C^{N} 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.

Open this publication in new window or tab >>Defect detection and classfiication: statistical learning approach - Part II### Pya Arnqvist, Natalya

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

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

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

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); ### Yu, Jun

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt184_7_j_idt188_j_idt202",{id:"formSmash:j_idt184:7:j_idt188:j_idt202",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_j_idt202",onLabel:"Hide others...",offLabel:"Show others..."}); 2019 (English)Report (Other academic)
##### Publisher

p. 56
##### Keywords

Statistical learning, probabilistic classification, defect detection, automated quality inspection
##### National Category

Probability Theory and Statistics Signal Processing Manufacturing, Surface and Joining Technology
##### Research subject

Mathematical Statistics
##### Identifiers

urn:nbn:se:umu:diva-161255 (URN)
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_j_idt371",{id:"formSmash:j_idt184:7:j_idt188:j_idt371",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_j_idt371",multiple:true});
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##### Funder

Vinnova, 2015-03706
Available from: 2019-07-01 Created: 2019-07-01 Last updated: 2019-07-19Bibliographically approved

Volvo Group Trucks Operations.

Open this publication in new window or tab >>Efficient surface finish defect detection using reduced rank spline smoothers### Pya Arnqvist, Natalya

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

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

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

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); ### Yu, Jun

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt184_8_j_idt188_j_idt202",{id:"formSmash:j_idt184:8:j_idt188:j_idt202",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_j_idt202",onLabel:"Hide others...",offLabel:"Show others..."}); 2019 (English)In: CRoNoS & MDA 2019, 2019Conference paper, Oral presentation with published abstract (Refereed)
##### Abstract [en]

##### National Category

Probability Theory and Statistics Signal Processing
##### Research subject

Mathematical Statistics
##### Identifiers

urn:nbn:se:umu:diva-158014 (URN)
##### Conference

CRoNoS & MDA2019, Cyprus, April 14-16, 2019
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##### Projects

FIQA
##### Funder

Vinnova, 2015-03706
Available from: 2019-04-10 Created: 2019-04-10 Last updated: 2019-04-16Bibliographically approved

Volvo Group Trucks Operations.

One of the primary concerns of product quality control in the automotive industry is an automated detection of defects of small sizes on specular car body surfaces. A new statistical learning approach is presented for surface finish defect detection based on spline smoothing method for feature extraction and k-nearest neighbor probabilistic classifier. Rather than analyzing the natural images of the car body surfaces, the deflectometry technique is applied for image acquisition. Reduced rank cubic regression splines are used to smooth the pixel values while the effective degrees of freedom of the obtained smooths serve as components of the feature vector. A key advantage of the approach is that it allows us to reach near zero misclassification error when applying standard learning classifiers. We also propose the probability based performance evaluation metrics as alternatives to the conventional metrics. The usage of those provides the means for uncertainty estimation of the predictive performance of a classifier. Experimental classification results on the images obtained from the pilot system located at Volvo cab plant in Umea, Sweden, show that the proposed approach is much more efficient than compared methods.

Open this publication in new window or tab >>Error bounds of block sparse signal recovery based on q-ratio block constrained minimal singular values### Wang, Jianfeng

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

### Yu, Jun

Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_some",{id:"formSmash:j_idt184:9:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_otherAuthors",{id:"formSmash:j_idt184:9:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: EURASIP Journal on Advances in Signal Processing, ISSN 1687-6172, E-ISSN 1687-6180, Vol. 2019, article id 57Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Springer, 2019
##### Keywords

Compressive sensing, q-ratio block sparsity, q-ratio block constrained minimal singular value, Convex-concave procedure
##### National Category

Signal Processing Probability Theory and Statistics Computational Mathematics
##### Research subject

Mathematical Statistics
##### Identifiers

urn:nbn:se:umu:diva-165632 (URN)10.1186/s13634-019-0653-1 (DOI)000499457500002 ()
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_j_idt371",{id:"formSmash:j_idt184:9:j_idt188:j_idt371",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_j_idt371",multiple:true});
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##### Funder

Swedish Research Council, 340-2013-5342
Available from: 2019-12-02 Created: 2019-12-02 Last updated: 2020-01-09Bibliographically approved

Department of Statistics, Zhejiang University City College, China.

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 ℓ_{2}/ℓ_{q} and the mixed ℓ_{2}/ℓ_{1} 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.

Wang, J., Zhou, Z. & Yu, J. (2020). Statistical inference for block sparsity of complex-valued signals. IET Signal ProcessingZhou, Z. & Yu, J. (2019). Adaptive estimation for varying coefficient modelswith nonstationary covariates. Communications in Statistics - Theory and Methods, 48(16), 4034-4050Leffler, K., Zhou, Z. & Yu, J. (2019). An extended block restricted isometry property for sparse recovery with non-Gaussian noise. Journal of Computational MathematicsWang, J., Zhou, Z., Garpebring, A. & Yu, J. (2019). Bayesian sparsity estimation in compressive sensing with application to MR images. Communications in Statistics: Case Studies, Data Analysis and Applications, 5(4), 415-431Wang, J., Zhou, Z. & Yu, J. (2019). Enhanced block sparse signal recovery based on q-ratio block constrained minimal singular values. Wang, J., Zhou, Z. & Yu, J. (2019). Error bounds of block sparse signal recovery based on q-ratio block constrained minimal singular values. EURASIP Journal on Advances in Signal Processing, 2019, Article ID 57. Zhou, Z. & Yu, J. (2019). On q-ratio CMSV for sparse recovery. Signal Processing, 165, 128-132Zhou, Z. & Yu, J. (2019). Phaseless compressive sensing using partial support information. Optimization LettersWang, J., Zhou, Z. & Yu, J. (2019). Statistical inference for block sparsity of complex signals.