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Open this publication in new window or tab >>A New Nonconvex Sparse Recovery Method for Compressive Sensing### 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}); 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.

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

### 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_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: 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

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

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_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: 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 >>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_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_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_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt184_3_j_idt188_j_idt202",{id:"formSmash:j_idt184:3:j_idt188:j_idt202",widgetVar:"widget_formSmash_j_idt184_3_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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##### 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_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_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_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); Show others...PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt184_4_j_idt188_j_idt202",{id:"formSmash:j_idt184:4:j_idt188:j_idt202",widgetVar:"widget_formSmash_j_idt184_4_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 >>Model-based computed tomography image estimation: partitioning approach### Bayisa, Fekadu

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_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 Applied Statistics, ISSN 0266-4763, E-ISSN 1360-0532Article in journal (Other (popular science, discussion, etc.)) Epub ahead of print
##### Abstract [en]

##### Keywords

Computed tomography; magnetic resonance imaging; CT image estimation; skew-Gaussian mixture model; Gaussian mixture model
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematical Statistics
##### Identifiers

urn:nbn:se:umu:diva-158259 (URN)10.1080/02664763.2019.1606169 (DOI)000465945500001 ()
#####

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Available from: 2019-04-17 Created: 2019-04-17 Last updated: 2019-05-28

There is a growing interest to get a fully MR based radiotherapy. The most important development needed is to obtain improved bone tissue estimation. The existing model-based methods perform poorly on bone tissues. This paper was aimed at obtaining improved bone tissue estimation. Skew-Gaussian mixture model and Gaussian mixture model were proposed to investigate CT image estimation from MR images by partitioning the data into two major tissue types. The performance of the proposed models was evaluated using the leaveone-out cross-validation method on real data. In comparison with the existing model-based approaches, the model-based partitioning approach outperformed in bone tissue estimation, especially in dense bone tissue estimation.

Open this publication in new window or tab >>On q-ratio CMSV for sparse recovery### 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_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: 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)
#####

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##### Funder

Swedish Research Council, 340-2013-5342
Available from: 2019-07-03 Created: 2019-07-03 Last updated: 2019-07-15

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 >>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 >>Sharper Positron Emission Tomography: Intelligent Data Sampling to Promote Accelerated Medical Imaging### Leffler, Klara

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

### Larsson, Anne

### Häggström, Ida

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)Conference paper, Poster (with or without abstract) (Other academic)
##### National Category

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

Mathematical Statistics
##### Identifiers

urn:nbn:se:umu:diva-157665 (URN)
##### Conference

Winter Conference in Statistics 2019 - Machine Learning, March 10-14, 2019, Hemavan, Sweden
#####

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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: 2019-03-28 Created: 2019-03-28 Last updated: 2019-04-12Bibliographically approved

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

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

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

Open 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_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: 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.

Zhou, Z. & Yu, J. (2019). Adaptive estimation for varying coefficient modelswith nonstationary covariates. Communications in Statistics - Theory and Methods, 48(16), 4034-4050Zhou, Z. & Yu, J. (2019). On q-ratio CMSV for sparse recovery. Signal Processing, 165, 128-132