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Zhou, Z. & Yu, J. (2019). A New Nonconvex Sparse Recovery Method for Compressive Sensing. Frontiers in Applied Mathematics and Statistics, 5, 1-11, Article ID 14.
Open this publication in new window or tab >>A New Nonconvex Sparse Recovery Method for Compressive Sensing
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]

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.

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)
Funder
Swedish Research Council, 340-2013-5342
Available from: 2019-03-15 Created: 2019-03-15 Last updated: 2019-03-20Bibliographically approved
Bayisa, F., Zhou, Z., Cronie, O. & Yu, J. (2019). Adaptive algorithm for sparse signal recovery. Digital signal processing (Print), 87, 10-18
Open this publication in new window or tab >>Adaptive algorithm for sparse signal recovery
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]

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.

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)
Projects
Statistical modelling and intelligent data sampling in MRI and PET measurements for cancer therapy assessment
Funder
Swedish Research Council, 340-2013-534
Note

Originally included in thesis in manuscript form

Available from: 2018-04-07 Created: 2018-04-07 Last updated: 2019-04-04Bibliographically approved
Zhou, Z. & Yu, J. (2019). Adaptive estimation for varying coefficient modelswith nonstationary covariates. Communications in Statistics - Theory and Methods, 48(16), 4034-4050
Open this publication in new window or tab >>Adaptive estimation for varying coefficient modelswith nonstationary covariates
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]

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.

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)
Funder
Swedish Research Council, 340-2013-534
Available from: 2018-12-30 Created: 2018-12-30 Last updated: 2019-08-06Bibliographically approved
Pya Arnqvist, N., Ngendangenzwa, B., Nilsson, L., Lindahl, E. & Yu, J. (2019). Defect detection and classfiication: statistical learning approach - Part II.
Open this publication in new window or tab >>Defect detection and classfiication: statistical learning approach - Part II
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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)
Funder
Vinnova, 2015-03706
Available from: 2019-07-01 Created: 2019-07-01 Last updated: 2019-07-19Bibliographically approved
Pya Arnqvist, N., Ngendangenzwa, B., Nilsson, L., Lindahl, E. & Yu, J. (2019). Efficient surface finish defect detection using reduced rank spline smoothers. In: CRoNoS & MDA 2019: . Paper presented at CRoNoS & MDA2019, Cyprus, April 14-16, 2019.
Open this publication in new window or tab >>Efficient surface finish defect detection using reduced rank spline smoothers
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2019 (English)In: CRoNoS & MDA 2019, 2019Conference paper, Oral presentation with published abstract (Refereed)
Abstract [en]

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.

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
Projects
FIQA
Funder
Vinnova, 2015-03706
Available from: 2019-04-10 Created: 2019-04-10 Last updated: 2019-04-16Bibliographically approved
Bayisa, F. & Yu, J. (2019). Model-based computed tomography image estimation: partitioning approach. Journal of Applied Statistics, 46(14), 2627-2648
Open this publication in new window or tab >>Model-based computed tomography image estimation: partitioning approach
2019 (English)In: Journal of Applied Statistics, ISSN 0266-4763, E-ISSN 1360-0532, Vol. 46, no 14, p. 2627-2648Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Taylor & Francis, 2019
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 ()
Available from: 2019-04-17 Created: 2019-04-17 Last updated: 2019-08-29Bibliographically approved
Zhou, Z. & Yu, J. (2019). On q-ratio CMSV for sparse recovery. Signal Processing, 165, 128-132
Open this publication in new window or tab >>On q-ratio CMSV for sparse recovery
2019 (English)In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 165, p. 128-132Article in journal (Refereed) Published
Abstract [en]

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 ℓ1-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.

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 ()
Funder
Swedish Research Council, 340-2013-5342
Available from: 2019-07-03 Created: 2019-07-03 Last updated: 2019-10-08Bibliographically approved
Zhou, Z. & Yu, J. (2019). Phaseless compressive sensing using partial support information. Optimization Letters
Open this publication in new window or tab >>Phaseless compressive sensing using partial support information
2019 (English)In: Optimization Letters, ISSN 1862-4472, E-ISSN 1862-4480Article in journal (Refereed) Epub ahead of print
Abstract [en]

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.

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)
Funder
Swedish Research Council, 340-2013-5342
Available from: 2019-10-07 Created: 2019-10-07 Last updated: 2019-10-09
Zhou, Z. & Yu, J. (2019). Recovery analysis for weighted mixed ℓ2/ℓp minimization with 0 < p ≤ 1. Journal of Computational and Applied Mathematics, 352, 210-222
Open this publication in new window or tab >>Recovery analysis for weighted mixed ℓ2/ℓp minimization with 0 < p ≤ 1
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]

We study the recovery conditions of weighted mixed ℓ2/ℓp (0 < p ≤ 1) minimization for block sparse signal reconstruction from compressed measurements when partial block support information is available. We show that the block p-restricted isometry property (RIP) can ensure the robust recovery. Moreover, we present the sufficient and necessary condition for the recovery by using weighted block p-null space property. The relationship between the block p-RIP and the weighted block p-null space property has been established. Finally, we illustrate our results with a series of numerical experiments.

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 ()
Projects
Statistical modelling and intelligent data sampling in MRI and PET measurements for cancer therapy assessment
Funder
Swedish Research Council, 340-2013-5342
Note

Originally included in thesis in manuscript form.

Available from: 2017-11-07 Created: 2017-11-07 Last updated: 2019-04-15Bibliographically approved
Leffler, K., Axelsson, J., Larsson, A., Häggström, I. & Yu, J. (2019). Sharper Positron Emission Tomography: Intelligent Data Sampling to Promote Accelerated Medical Imaging. In: : . Paper presented at Winter Conference in Statistics 2019 - Machine Learning, March 10-14, 2019, Hemavan, Sweden.
Open this publication in new window or tab >>Sharper Positron Emission Tomography: Intelligent Data Sampling to Promote Accelerated Medical Imaging
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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
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
Projects
Statistical modelling and intelligent data sampling in MRI and PET measurements for cancer therapy assessment [2013-05342_VR]; Umeå University; Publications
Zhou, 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. & Yu, J. (2019). Enhanced block sparse signal recovery based on q-ratio block constrained minimal singular values. 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.
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0001-5673-620x

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