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Zhou, Zhiyong

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

### Zhou, Zhiyong

### Yu, Jun

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}); 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}); 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.

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 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

### 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}); 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

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

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_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: 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_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: 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 >>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_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: 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 >>On q-ratio CMSV for sparse recovery### 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: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 165, p. 128-132Article in journal (Refereed) Published
##### Abstract [en]

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

Elsevier, 2019
##### Keywords

Sparse recovery, q-ratio sparsity, q-ratio constrained minimal singular values, ℓ1-truncated set q-width
##### National Category

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

Mathematical Statistics
##### Identifiers

urn:nbn:se:umu:diva-161379 (URN)10.1016/j.sigpro.2019.07.003 (DOI)000485855000012 ()
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##### Funder

Swedish Research Council, 340-2013-5342
Available from: 2019-07-03 Created: 2019-07-03 Last updated: 2019-11-11Bibliographically approved

As a kind of computable incoherence measure of the measurement matrix, *q*-ratio constrained minimal singular values (CMSV) was proposed in Zhou and Yu (2019) to derive the performance bounds for sparse recovery. In this paper, we study the geometrical properties of the *q*-ratio CMSV, based on which we establish new sufficient conditions for signal recovery involving both sparsity defect and measurement error. The ℓ_{1}-truncated set *q*-width of the measurement matrix is developed as the geometrical characterization of *q*-ratio CMSV. In addition, we show that the *q*-ratio CMSVs of a class of structured random matrices are bounded away from zero with high probability as long as the number of measurements is large enough, therefore these structured random matrices satisfy those established sufficient conditions. Overall, our results generalize the results in Zhang and Cheng (2012) from q=2 to any *q* ∈ (1, ∞] and complement the arguments of *q*-ratio CMSV from a geometrical view.

Open this publication in new window or tab >>Phaseless compressive sensing using partial support information### Zhou, Zhiyong

### 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: Optimization Letters, ISSN 1862-4472, E-ISSN 1862-4480Article in journal (Refereed) Epub ahead of print
##### Abstract [en]

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

Springer, 2019
##### Keywords

Phaseless compressive sensing, Partial support information, Strong restricted isometry property, Weighted null space property
##### National Category

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

Mathematical Statistics
##### Identifiers

urn:nbn:se:umu:diva-163880 (URN)10.1007/s11590-019-01487-w (DOI)
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##### Funder

Swedish Research Council, 340-2013-5342
Available from: 2019-10-07 Created: 2019-10-07 Last updated: 2019-10-09

Department of Statistics, Zhejiang University City College, China.

We study the recovery conditions of weighted ℓ1 minimization for real-valued signal reconstruction from phaseless compressive sensing measurements when partial support information is available. A strong restricted isometry property condition is provided to ensure the stable recovery. Moreover, we present the weighted null space property as the sufficient and necessary condition for the success of k-sparse phaseless recovery via weighted ℓ1 minimization. Numerical experiments are conducted to illustrate our results.

Open this publication in new window or tab >>Recovery analysis for weighted mixed ℓ_{2}/ℓ_{p} minimization with 0 < *p* ≤ 1### 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_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); 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}); 2019 (English)In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 352, p. 12p. 210-222Article in journal (Refereed) Published
##### Abstract [en]

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

Elsevier, 2019. p. 12
##### Keywords

Compressive sensing, Prior support information, Block sparse, Non-convex minimization
##### National Category

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

Mathematical Statistics
##### Identifiers

urn:nbn:se:umu:diva-141543 (URN)10.1016/j.cam.2018.11.031 (DOI)000458713000015 ()
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##### Projects

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

Swedish Research Council, 340-2013-5342
##### Note

We study the recovery conditions of weighted mixed ℓ_{2}/ℓ* _{p}* (0 <

Originally included in thesis in manuscript form.

Available from: 2017-11-07 Created: 2017-11-07 Last updated: 2019-04-15Bibliographically approvedOpen this publication in new window or tab >>Sparse recovery based on *q*-ratio constrained minimal singular values### 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_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); 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}); 2019 (English)In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 155, p. 247-258Article in journal (Refereed) Published
##### Abstract [en]

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

Elsevier, 2019
##### Keywords

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

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

Mathematical Statistics; Signal Processing
##### Identifiers

urn:nbn:se:umu:diva-152530 (URN)10.1016/j.sigpro.2018.10.002 (DOI)000452585600019 ()2-s2.0-85054424540 (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
Available from: 2018-10-10 Created: 2018-10-10 Last updated: 2019-02-28Bibliographically approved

We study verifiable sufficient conditions and computable performance bounds for sparse recovery algorithms such as the Basis Pursuit, the Dantzig selector and the Lasso estimator, in terms of a newly defined family of quality measures for the measurement matrices. With high probability, the developed measures for subgaussian random matrices are bounded away from zero as long as the number of measurements is reasonably large. Comparing to the restricted isotropic constant based performance analysis, the arguments in this paper are much more concise and the obtained bounds are tighter. Numerical experiments are presented to illustrate our theoretical results.

Open this publication in new window or tab >>Stable and robust ℓ_{p}-constrained compressive sensing recovery via robust width property### Yu, Jun

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.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: Journal of the Korean Mathematical Society, ISSN 0304-9914, E-ISSN 2234-3008, Vol. 56, no 3, p. 689-701Article in journal (Refereed) Published
##### Abstract [en]

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

Korean Mathematical Society, 2019
##### Keywords

compressive sensing, robust width property, robust null space property, restricted isometry property
##### National Category

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

Mathematical Statistics
##### Identifiers

urn:nbn:se:umu:diva-158390 (URN)10.4134/JKMS.j180321 (DOI)000466041600006 ()
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_j_idt359",{id:"formSmash:j_idt184:9:j_idt188:j_idt359",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_j_idt359",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_j_idt365",{id:"formSmash:j_idt184:9:j_idt188:j_idt365",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_j_idt365",multiple:true});
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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});
#####

##### Projects

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

Swedish Research Council, 340-2013-5342
Available from: 2019-04-26 Created: 2019-04-26 Last updated: 2019-06-12Bibliographically approved

We study the recovery results of ℓ* _{p}*-constrained compressive sensing (CS) with p≥1 via robust width property and determine conditions on the number of measurements for standard Gaussian matrices under which the property holds with high probability. Our paper extendsthe existing results in Cahill and Mixon [2] from ℓ2-constrained CS to ℓ