[{"_id":"project:1299","_type":"project","abstract":{"sv":"In general, most bio-imaging (imaging resulting in images that represent actual biological quantities, e.g., perfusion) is limited by noise, resolution, motion artifacts etc., but at the same time heavily oversampled with respect to the information relevant for the actual purpose. The purpose of this project is to develop new statistical and computational methodology for intelligent data sampling and uncertainty analysis of MRI and PET measurements. More specific, statistical spatiotemporal models to characterize stochastic noise in parametric imaging based on MRI and PET will be developed and, for the same techniques, intelligent data sampling based on Compressed Sensing will be investigated. Focus will be on the statistical and computational challenges arising from uncertainty analysis and error versus speed optimization for high-dimensional data.    This project should contribute to the general understanding of optimised data sampling in bio-imaging and to efficient noise reduction for improved quality of the estimated parametric images. When applied in therapy response imaging this project should result in significantly shorter imaging time and more reliable quantitative information which are two important steps in bringing bio-imaging towards a more widespread clinical use."},"project_id":"2013-05342_VR","identifier_short":"2013-05342","dates":{"start_date":"2014-01-01","end_date":"2017-12-31"},"organizations":[{"funding":[{"_id":2,"id":"202100-5208","sv":"Vetenskapsrådet","en":"Swedish Research Council"}]},{"coordinating":[{"_id":715,"id":"202100-2874","sv":"Umeå universitet","en":"Umeå University"}]}],"people":[{"project_leaders":[{"_id":"authority-person:63104","orcid":"0000-0001-5673-620X","name":"Yu, Jun","role":"principal_investigator","affiliation":[{"_id":715,"id":"202100-2874","sv":"Umeå universitet","en":"Umeå University"}]}]},{"other_personnel":[]}],"tags":[{"_id":11507,"id":"10106","sv":"Sannolikhetsteori och statistik","en":"Probability Theory and Statistics"},{"_id":11614,"id":"20603","sv":"Medicinsk bildbehandling","en":"Medical Image Processing"},{"_id":11665,"id":"30203","sv":"Cancer och onkologi","en":"Cancer and Oncology"}],"titles":{"sv":"Statistiska modeller och intelligenta datainsamlingsmetoder för MRI och PET mätningar med tillämpning för monitoring av cancerbehandling","en":"Statistical modelling and intelligent data sampling in MRI and PET measurements for cancer therapy assessment"},"total_funding":"5500000","type_of_awards":{"sv":"Projektbidrag","en":"Project grant"},"publications":[{"id":"diva2:1834759","type":"manuscript","issued":{"date-parts":[[2024]]},"title":"A ridgelet approach to poisson denoising","language":"eng","author":[{"family":"Dadras","given":"Ali","localId":"alda0079","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]},{"family":"Leffler","given":"Klara","ORCID":"0000-0002-5130-1941","localId":"klle0001","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]},{"family":"Yu","given":"Jun","ORCID":"0000-0001-5673-620X","localId":"juyu0002","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]}],"abstract":"This paper introduces a novel ridgelet transform-based method for Poisson image denoising. Our work focuses on harnessing the Poisson noise's unique non-additive and signal-dependent properties, distinguishing it from Gaussian noise. The core of our approach is a new thresholding scheme informed by theoretical insights into the ridgelet coefficients of Poisson-distributed images and adaptive thresholding guided by Stein's method. We verify our theoretical model through numerical experiments and demonstrate the potential of ridgelet thresholding across assorted scenarios. Our findings represent a significant step in enhancing the understanding of Poisson noise and offer an effective denoising method for images corrupted with it.","ISBN":"978-91-8070-279-9","DOI":"10.48550/arXiv.2401.16099","NBN":"urn:nbn:se:umu:diva-220205","keyword":"sparse signal processing; compressed sensing; positron emission tomography; denoising; inpainting","published":[{"raw":"2024-02-05T15:18:46.872+01:00"}],"created":[{"raw":"2024-02-05T15:18:46.949+01:00"}],"updated":[{"raw":"2024-02-06T11:01:19.153+01:00"}],"URL":"https://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-220205"},{"id":"diva2:1834782","type":"thesis","genre":"PhD dissertation","issued":{"date-parts":[[2024]]},"title":"The PET sampling puzzle : intelligent data sampling methods for positron emission tomography","language":"eng","author":[{"family":"Leffler","given":"Klara","ORCID":"0000-0002-5130-1941","localId":"klle0001","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]}],"supervisor":[{"family":"Yu","given":"Jun","ORCID":"0000-0001-5673-620X","localId":"juyu0002","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]},{"family":"Häggström","given":"Ida","affiliation":[{"name":"Department of Electrical Engineering, Chalmers University of Technology, Gothenburg, Sweden"}]},{"family":"Zhou","given":"Zhiyong","affiliation":[{"name":"Department of Statistics and Data Science, Hangzhou City University, Hangzhou, China"}]}],"opponent":[{"family":"Chatterjee","given":"Saikat","affiliation":[{"name":"Institutionen för intelligenta system, Kungliga tekniska högskolan, Stockholm, Sverige"}]}],"abstract":"Much like a backwards computed Sudoku puzzle, starting from the completed number grid and working ones way down to a partially completed grid without damaging the route back to the full unique solution, this thesis tackles the challenges behind setting up a number puzzle in the context of biomedical imaging. By leveraging sparse signal processing theory, we study the means of practical undersampling of positron emission tomography (PET) measurements, an imaging modality in nuclear medicine that visualises functional processes within the body using radioactive tracers. What are the rules for measurement removal? How many measurements can be removed without damaging the route back to the full solution? Moreover, how is the original solution retained once the data has been altered? This thesis aims to investigate and answer such questions in relation to PET data sampling, thereby creating a foundation for a PET Sampling Puzzle.The objective is to develop intelligent data sampling strategies that allow for practical undersampling of PET measurements combined with sophisticated computational compensations to address the resulting data distortions. We focus on two main challenges in PET undersampling: low-count measurements due to reduced radioactive dose or reduced scan times and incomplete measurements from sparse PET detector configurations. The methodological framework is based on key aspects of sparse signal processing: sparse representations, sparsity patterns and sparse signal recovery, encompassing denoising and inpainting. Following the characteristics of PET measurements, all elements are considered with an underlying assumption of signal-dependent Poisson distributed noise.The results demonstrate the potential of noise awareness, sparsity, and deep learning to enhance and restore measurements corrupted with signal-dependent Poisson distributed noise, such as those in PET imaging, thereby marking a notable step towards unravelling the PET Sampling Puzzle.","ISBN":"9789180702799","NBN":"urn:nbn:se:umu:diva-220515","number-of-pages":"30","collection-title":"Research report in mathematical statistics","collection-number":"76/24","keyword":"sparse signal processing; compressed sensing; Poisson denoising; positron emission tomography (PET); sinogram denoising; sinogram inpainting; deep learning","publisher-place":"Umeå","publisher":"Umeå University","published":[{"raw":"2024-02-08T07:00:00.000+01:00"}],"created":[{"raw":"2024-02-05T15:48:47.568+01:00"}],"updated":[{"raw":"2025-02-09T05:20:22.156+01:00"}],"URL":"https://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-220515"},{"id":"diva2:1860564","type":"paper-conference","issued":{"date-parts":[[2023]]},"title":"Compressed sensing for low-count PET denoising in measurement space","language":"eng","author":[{"family":"Leffler","given":"Klara","ORCID":"0000-0002-5130-1941","localId":"klle0001","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]},{"family":"Häggström","given":"Ida","affiliation":[{"name":"Department of Electrical Engineering, Chalmers University of Technology, Gothenburg, Sweden"}]},{"family":"Yu","given":"Jun","ORCID":"0000-0001-5673-620X","localId":"juyu0002","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]}],"abstract":"Low-count positron emission tomography (PET) data suffer from high noise levels, leading topoor image quality and reduced diagnostic accuracy. Compressed sensing (CS) based denoisingmethods have shown potential in medical imaging. This study investigates the performance ofCS-based denoising methods on PET sinograms.Three simulated datasets were used in this study, including circular phantom, patient pelvisphantom, and patient brain phantom. Ten sampling levels were employed to investigate the effect of data reduction on diagnostic accuracy. CS-based denoising methods were applied prereconstruction, and a conventional Gaussian post-filter was used for comparison. Performancemeasures included rRMSE, SSIM, SNR, line profiles, and FWHM.Overall, the proposed CS-based denoising methods performed similarly to the benchmark interms of lesion contrast, spatial resolution, and noise texture. The proposed methods outperformed the benchmark in low-count situations by suppressing background noise and preservingcontrast better.The results of this study demonstrate that CS-based denoising methods in the sinogram domain can improve the quality of low-count PET images, particularly in suppressing backgroundnoise and preserving contrast. These findings suggest that CS-based denoising could be apromising solution for improving the diagnostic accuracy of low-count PET data.","NBN":"urn:nbn:se:umu:diva-224907","container-title":"NORDSTAT 2023 Gothenburg","event":"The 29th Nordic Conference in Mathematical Statistics, Gothenburg, Sweden, June 19-22, 2023.","publisher":"Göteborgs universitet","published":[{"raw":"2024-05-24T13:20:00.000+02:00"}],"created":[{"raw":"2024-05-24T13:20:26.397+02:00"}],"updated":[{"raw":"2025-02-09T05:19:06.345+01:00"}],"URL":"https://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-224907"},{"id":"diva2:1860574","type":"paper-conference","issued":{"date-parts":[[2023]]},"title":"Deep learning-based filling of incomplete sinograms from low-cost, long axial field-of-view PET scanners with inter-detector gaps","language":"eng","author":[{"family":"Leffler","given":"Klara","ORCID":"0000-0002-5130-1941","localId":"klle0001","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]},{"family":"Tommaso Luppino","given":"Luigi","affiliation":[{"name":"Department Physics and Technology, UiT The Arctic University of Norway, Tromsø, Norway"}]},{"family":"Kuttner","given":"Samuel","affiliation":[{"name":"University Hospital of North Norway, Tromsø, Norway; Physics and Technology, UiT The Arctic University of Norway, Tromsø, Norway; Department of Clinical Medicine, UiT The Arctic University of Norway, Tromsø, Norway."}]},{"family":"Axelsson","given":"Jan","ORCID":"0000-0002-3731-3612","localId":"jaax0004","affiliation":[{"id":"889252","name":"Umeå universitet, Institutionen för diagnostik och intervention"}]}],"NBN":"urn:nbn:se:umu:diva-224909","page":"59-59","container-title":"The international networking symposiumon artificial intelligence and informatics in nuclear medicine : Program book","event":"International Symposium on Artificial Intelligence and Informatics in Nuclear Medicine, Groningen, Netherlands, October 9-11, 2023.","keyword":"positron emission tomography (PET); sparse PET; deep learning - artificial intelligence; residual U-net; gap filling; long axial field of view PET; total body PET","publisher":"University Medical Center Groningen","published":[{"raw":"2024-05-24T13:35:00.000+02:00"}],"created":[{"raw":"2024-05-24T13:35:15.333+02:00"}],"updated":[{"raw":"2025-02-09T05:19:04.993+01:00"}],"URL":"https://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-224909"},{"id":"diva2:1699817","type":"article-journal","status":"Published","issued":{"date-parts":[[2022]]},"title":"Estimation of block sparsity in compressive sensing","language":"eng","author":[{"family":"Zhou","given":"Zhiyong","ORCID":"0000-0001-9861-6134","affiliation":[{"name":"Department of Statistics and Data Science, Institute of Digital Finance, Zhejiang University City College, Hangzhou 310015, P. R. China"}]},{"family":"Yu","given":"Jun","ORCID":"0000-0001-5673-620X","localId":"juyu0002","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]}],"abstract":"Explicitly using the block structure of the unknown signal can achieve better reconstruction performance in compressive sensing. An unknown signal with block structure can be accurately recovered from under-determined linear measurements provided that it is sufficiently block sparse. However, in practice, the block sparsity level is typically unknown. In this paper, we propose a soft measure of block sparsity k<sub>α</sub>(x) = (||x||<sub>2,α</sub>/||x||<sub>2,1</sub>) <sup>α/(1−α) </sup>with α ∈ [0,∞], and present a procedure to estimate it by using multivariate centered isotropic symmetric α-stable random projections. The limiting distribution of the estimator is given. Simulations are conducted to illustrate our theoretical results.","DOI":"10.1142/s0219691322500345","ScopusId":"2-s2.0-85136582237","NBN":"urn:nbn:se:umu:diva-199809","issue":"06","volume":"20","number":"2250034","container-title":"International Journal of Wavelets, Multiresolution and Information Processing","ISSN":"1793-690X","keyword":"Compressive sensing; block sparsity; multivariate centered isotropic symmetric α-stable distribution; characteristic function","publisher":"World Scientific","published":[{"raw":"2022-09-29T09:19:00.000+02:00"}],"created":[{"raw":"2022-09-29T09:19:45.006+02:00"}],"updated":[{"raw":"2022-10-19T11:10:06.691+02:00"}],"URL":"https://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-199809"},{"id":"diva2:1155144","type":"article-journal","status":"Published","issued":{"date-parts":[[2021]]},"title":"Contrast Agent Quantification by Using Spatial Information in Dynamic Contrast Enhanced MRI","language":"eng","author":[{"family":"Wang","given":"Jianfeng","ORCID":"0000-0002-9341-1137","localId":"jiwa0016","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]},{"family":"Garpebring","given":"Anders","ORCID":"0000-0002-0532-232X","localId":"anga0014","affiliation":[{"id":"779","name":"Umeå universitet, Radiofysik"}]},{"family":"Brynolfsson","given":"Patrik","localId":"pakbon02","affiliation":[{"id":"779","name":"Umeå universitet, Radiofysik"}]},{"family":"Yu","given":"Jun","ORCID":"0000-0001-5673-620X","localId":"juyu0002","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]}],"abstract":"The purpose of this work is to investigate spatial statistical modelling approaches to improve contrast agent quantification in dynamic contrast enhanced MRI, by utilising the spatial dependence among image voxels. Bayesian hierarchical models (BHMs), such as Besag model and Leroux model, were studied using simulated MRI data. The models were built on smaller images where spatial dependence can be incorporated, and then extended to larger images using the maximum a posteriori (MAP) method. Notable improvements on contrast agent concentration estimation were obtained for both smaller and larger images. For smaller images: the BHMs provided substantial improved estimates in terms of the root mean squared error (rMSE), compared to the estimates from the existing method for a noise level equivalent of a 12-channel head coil at 3T. Moreover, Leroux model outperformed Besag models with two different dependence structures. Specifically, the Besag models increased the estimation precision by 27% around the peak of the dynamic curve, while the Leroux model improved the estimation by 40% at the peak, compared with the existing estimation method. For larger images: the proposed MAP estimators showed clear improvements on rMSE for vessels, tumor rim and white matter.","DOI":"10.3389/frsip.2021.727387","ScopusId":"2-s2.0-85212500211","NBN":"urn:nbn:se:umu:diva-141525","volume":"1","number-of-pages":"12","number":"727387","container-title":"Frontiers in Signal Processing","ISSN":"2673-8198","keyword":"Contrast agent quantication; BHM; Besag; Leroux; INLA; MAP","publisher":"Frontiers Media S.A.","note":"Originally included in thesis in manuscript form.","published":[{"raw":"2017-11-07T09:43:00.000+01:00"}],"created":[{"raw":"2017-11-07T09:43:50.497+01:00"}],"updated":[{"raw":"2025-02-09T05:45:38.815+01:00"}],"URL":"https://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-141525"},{"id":"diva2:1582653","type":"article-journal","status":"Published","issued":{"date-parts":[[2021]]},"title":"Minimization of the <i>q</i>-ratio sparsity with 1 <i>&lt; </i><i>q </i>≤∞ for signal recovery","language":"eng","author":[{"family":"Zhou","given":"Zhiyong","affiliation":[{"name":"Department of Statistics, Zhejiang University City College, China"}]},{"family":"Yu","given":"Jun","ORCID":"0000-0001-5673-620X","localId":"juyu0002","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]}],"abstract":"In this paper, we propose a general scale invariant approach for sparse signal recovery via the minimization of the q-ratio sparsity s<sub>q</sub>(z) = (||z||<sub>1 </sub>/ ||z||<sub>q</sub> )<sup>q/(q-1) </sup>with q ∈ [0 , ∞]. The properties of the q-ratio sparsity measure are studied and illustrated with examples. For the proposed q-ratio sparsity minimization problem with 1 &lt; q ≤∞ , we establish a verifiable exact reconstruction condition and derive its concise error bounds in terms of q-ratio constrained minimal singular values (CMSV). From an algorithmic point of view, we recognize that the proposed problem belongs to the nonlinear fractional programming and investigate two kinds of methods for solving it including the parametric methods and the change of variable method. Numerical experiments are conducted to demonstrate the advantageous performance of the proposed approaches over the state-of-the-art sparse recovery methods. ","DOI":"10.1016/j.sigpro.2021.108250","ScopusId":"2-s2.0-85111599813","NBN":"urn:nbn:se:umu:diva-186464","volume":"189","number":"108250","container-title":"Signal Processing","ISSN":"1872-7557","keyword":"Compressive sensing; q-ratio sparsity; q-ratio CMSV; Nonlinear fractional programming; Convex-concave procedure","publisher":"Elsevier","published":[{"raw":"2021-08-03T10:27:00.000+02:00"}],"created":[{"raw":"2021-08-03T10:27:49.205+02:00"}],"updated":[{"raw":"2023-09-05T09:02:52.197+02:00"}],"URL":"https://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-186464"},{"id":"diva2:1351857","type":"article-journal","status":"Published","issued":{"date-parts":[[2020]]},"title":"An extended block restricted isometry property for sparse recovery with non-Gaussian noise","language":"eng","author":[{"family":"Leffler","given":"Klara","ORCID":"0000-0002-5130-1941","localId":"klle0001","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]},{"family":"Zhou","given":"Zhiyong","affiliation":[{"name":"Department of Statistics, Zhejiang University City College, China"}]},{"family":"Yu","given":"Jun","ORCID":"0000-0001-5673-620X","localId":"juyu0002","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]}],"abstract":"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.","DOI":"10.4208/jcm.1905-m2018-0256","ScopusId":"2-s2.0-85092354908","NBN":"urn:nbn:se:umu:diva-163366","issue":"6","volume":"38","page":"827-838","container-title":"Journal of Computational Mathematics","ISSN":"1991-7139","keyword":"Compressed sensing; block sparsity; partial support information; signal reconstruction; convex optimization","publisher":"Global Science Press","published":[{"raw":"2019-09-17T08:44:00.000+02:00"}],"created":[{"raw":"2019-09-17T08:44:14.152+02:00"}],"updated":[{"raw":"2024-02-06T11:08:57.203+01:00"}],"URL":"https://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-163366"},{"id":"diva2:1474259","type":"manuscript","issued":{"date-parts":[[2020]]},"title":"Minimization of the q-ratio sparsity with 1&lt;q≤∞ for signal recovery","language":"eng","author":[{"family":"Zhou","given":"Zhiyong","affiliation":[{"name":"Department of Statistics, Zhejiang University City College, China"}]},{"family":"Yu","given":"Jun","ORCID":"0000-0001-5673-620X","localId":"juyu0002","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]}],"abstract":"In this paper, we propose a general scale invariant approach for sparse signal recovery via the minimization of the q-ratio sparsity. When 1&lt;q≤∞, both the theoretical analysis based on q-ratio constrained minimal singular values (CMSV) and the practical algorithms via nonlinear fractional programming are presented. Numerical experiments are conducted to demonstrate the advantageous performance of the proposed approaches over the state-of-the-art sparse recovery methods.","NBN":"urn:nbn:se:umu:diva-175761","number-of-pages":"21","keyword":"Compressive sensing; q-ratio sparsity; q-ratio CMSV; nonlinear fractional programming; convex-concave procedure","published":[{"raw":"2020-10-08T09:26:00.000+02:00"}],"created":[{"raw":"2020-10-08T09:26:01.602+02:00"}],"updated":[{"raw":"2020-10-08T09:46:24.061+02:00"}],"URL":"https://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-175761"},{"id":"diva2:1358083","type":"article-journal","status":"Published","issued":{"date-parts":[[2020]]},"title":"Phaseless compressive sensing using partial support information","language":"eng","author":[{"family":"Zhou","given":"Zhiyong","localId":"zhzh0022","affiliation":[{"name":"Department of Statistics, Zhejiang University City College, China"}]},{"family":"Yu","given":"Jun","ORCID":"0000-0001-5673-620X","localId":"juyu0002","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]}],"abstract":"We study the recovery conditions of weighted ℓ<sub>1</sub> 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 <i>k</i>-sparse phaseless recovery via weighted ℓ<sub>1</sub> minimization. Numerical experiments are conducted to illustrate our results.","DOI":"10.1007/s11590-019-01487-w","ScopusId":"2-s2.0-85076540554","NBN":"urn:nbn:se:umu:diva-163880","volume":"14","page":"1961-1973","container-title":"Optimization Letters","ISSN":"1862-4480","keyword":"Phaseless compressive sensing; Partial support information; Strong restricted isometry property; Weighted null space property","publisher":"Springer","published":[{"raw":"2019-10-07T09:33:00.000+02:00"}],"created":[{"raw":"2019-10-07T09:33:18.862+02:00"}],"updated":[{"raw":"2021-10-19T16:06:49.419+02:00"}],"URL":"https://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-163880"},{"id":"diva2:1392716","type":"article-journal","status":"Published","issued":{"date-parts":[[2020]]},"title":"Statistical inference for block sparsity of complex-valued signals","language":"eng","author":[{"family":"Wang","given":"Jianfeng","ORCID":"0000-0002-9341-1137","localId":"jiwa0016","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]},{"family":"Zhou","given":"Zhiyong","localId":"zhzh0022","affiliation":[{"name":"Department of Statistics, Zhejiang University City College, China"},{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]},{"family":"Yu","given":"Jun","ORCID":"0000-0001-5673-620X","localId":"juyu0002","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]}],"abstract":"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.","DOI":"10.1049/iet-spr.2019.0200","ScopusId":"2-s2.0-85084180510","NBN":"urn:nbn:se:umu:diva-168016","issue":"3","volume":"14","page":"154-161","container-title":"IET Signal Processing","ISSN":"1751-9683","keyword":"Block sparsity; Complex-valued signals; Multivariate isotropic symmetric alpha-stable distributions","publisher":"Institution of Engineering and Technology","published":[{"raw":"2020-02-10T09:02:00.000+01:00"}],"created":[{"raw":"2020-02-10T09:02:04.375+01:00"}],"updated":[{"raw":"2023-03-23T15:20:39.086+01:00"}],"URL":"https://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-168016"},{"id":"diva2:1274392","type":"article-journal","status":"Published","issued":{"date-parts":[[2019]]},"title":"Adaptive estimation for varying coefficient modelswith nonstationary covariates","language":"eng","author":[{"family":"Zhou","given":"Zhiyong","localId":"zhzh0022","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]},{"family":"Yu","given":"Jun","ORCID":"0000-0001-5673-620X","localId":"juyu0002","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]}],"abstract":"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.","DOI":"10.1080/03610926.2018.1484483","ScopusId":"2-s2.0-85059303429","NBN":"urn:nbn:se:umu:diva-154754","issue":"16","volume":"48","page":"4034-4050","container-title":"Communications in Statistics - Theory and Methods","ISSN":"1532-415X","keyword":"Varying coefficient model; adaptive estimation; local linear fitting; non stationary covariates","publisher":"Taylor & Francis","published":[{"raw":"2018-12-30T13:52:00.000+01:00"}],"created":[{"raw":"2018-12-30T13:52:55.541+01:00"}],"updated":[{"raw":"2023-03-24T14:52:52.657+01:00"}],"URL":"https://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-154754"},{"id":"diva2:1367986","type":"article-journal","status":"Published","issued":{"date-parts":[[2019]]},"title":"Bayesian sparsity estimation in compressive sensing with application to MR images","language":"eng","author":[{"family":"Wang","given":"Jianfeng","ORCID":"0000-0002-9341-1137","localId":"jiwa0016","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]},{"family":"Zhou","given":"Zhiyong","localId":"zhzh0022","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]},{"family":"Garpebring","given":"Anders","ORCID":"0000-0002-0532-232X","localId":"anga0014","affiliation":[{"id":"779","name":"Umeå universitet, Radiofysik"}]},{"family":"Yu","given":"Jun","ORCID":"0000-0001-5673-620X","localId":"juyu0002","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]}],"abstract":"The theory of compressive sensing (CS) asserts that an unknownsignal <b>x</b> ∈ C<sup>N</sup> can be accurately recovered from m measurements with m « N provided that <b>x</b> is sparse. Most of the recovery algorithms need the sparsity s = ||<b>x</b>||<sub>0</sub> 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.","DOI":"10.1080/23737484.2019.1675557","NBN":"urn:nbn:se:umu:diva-164952","issue":"4","volume":"5","page":"415-431","container-title":"Communications in Statistics: Case Studies, Data Analysis and Applications","ISSN":"2373-7484","keyword":"Compressive sensing; sparsity; Bayesian hierarchical model; Matérn covariance; MRI","publisher":"Taylor & Francis Group","published":[{"raw":"2019-11-05T14:16:00.000+01:00"}],"created":[{"raw":"2019-11-05T14:16:01.087+01:00"}],"updated":[{"raw":"2025-02-09T05:37:24.363+01:00"}],"URL":"https://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-164952"},{"id":"diva2:1348154","type":"manuscript","issued":{"date-parts":[[2019]]},"title":"Enhanced block sparse signal recovery based on q-ratio block constrained minimal singular values","language":"eng","author":[{"family":"Wang","given":"Jianfeng","ORCID":"0000-0002-9341-1137","localId":"jiwa0016","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]},{"family":"Zhou","given":"Zhiyong","affiliation":[{"name":"Department of Statistics, Zhejiang University City College, Hangzhou, China"}]},{"family":"Yu","given":"Jun","ORCID":"0000-0001-5673-620X","localId":"juyu0002","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]}],"abstract":"In this paper we introduce theq-ratio block constrained minimal singular values (BCMSV) as a new measure of measurement matrix in compressive sensing of block sparse/compressive signals and present an algorithm for computing this new measure. Both the mixed ℓ2/ℓq and the mixed ℓ2/ℓ1 norms of the reconstruction errors for stable and robust recovery using block Basis Pursuit (BBP), the block Dantzig selector (BDS) and the group lasso in terms of the q-ratio BCMSV are investigated. We establish a sufficient condition based on the q-ratio block sparsity for the exact recovery from the noise free BBP and developed a convex-concave procedure to solve the corresponding non-convex problem in the condition. Furthermore, we prove that for sub-Gaussian random matrices, theq-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.","NBN":"urn:nbn:se:umu:diva-162953","number-of-pages":"20","keyword":"Compressive sensing;q-ratio block sparsity;q-ratio block constrained minimal singularvalue; Convex-concave procedure","published":[{"raw":"2019-09-03T14:35:55.781+02:00"}],"created":[{"raw":"2019-09-03T14:35:55.869+02:00"}],"updated":[{"raw":"2021-09-14T14:17:00.196+02:00"}],"URL":"https://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-162953"},{"id":"diva2:1374655","type":"article-journal","status":"Published","issued":{"date-parts":[[2019]]},"title":"Error bounds of block sparse signal recovery based on q-ratio block constrained minimal singular values","language":"eng","author":[{"family":"Wang","given":"Jianfeng","ORCID":"0000-0002-9341-1137","localId":"jiwa0016","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]},{"family":"Zhou","given":"Zhiyong","affiliation":[{"name":"Department of Statistics, Zhejiang University City College, China"}]},{"family":"Yu","given":"Jun","ORCID":"0000-0001-5673-620X","localId":"juyu0002","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]}],"abstract":"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<sub>2</sub>/ℓ<sub>q</sub> and the mixed ℓ<sub>2</sub>/ℓ<sub>1</sub> 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.","DOI":"10.1186/s13634-019-0653-1","ScopusId":"2-s2.0-85075673271","NBN":"urn:nbn:se:umu:diva-165632","volume":"2019","number":"57","container-title":"EURASIP Journal on Advances in Signal Processing","ISSN":"1687-6180","keyword":"Compressive sensing; q-ratio block sparsity; q-ratio block constrained minimal singular value; Convex-concave procedure","publisher":"Springer","published":[{"raw":"2019-12-02T13:43:00.000+01:00"}],"created":[{"raw":"2019-12-02T13:43:44.304+01:00"}],"updated":[{"raw":"2023-03-23T16:28:19.307+01:00"}],"URL":"https://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-165632"},{"id":"diva2:1334627","type":"article-journal","status":"Published","issued":{"date-parts":[[2019]]},"title":"On q-ratio CMSV for sparse recovery","language":"eng","author":[{"family":"Zhou","given":"Zhiyong","localId":"zhzh0022"},{"family":"Yu","given":"Jun","ORCID":"0000-0001-5673-620X","localId":"juyu0002","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]}],"abstract":"As a kind of computable incoherence measure of the measurement matrix, <i>q</i>-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 <i>q</i>-ratio CMSV, based on which we establish new sufficient conditions for signal recovery involving both sparsity defect and measurement error. The ℓ<sub>1</sub>-truncated set <i>q</i>-width of the measurement matrix is developed as the geometrical characterization of <i>q</i>-ratio CMSV. In addition, we show that the <i>q</i>-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 <i>q</i> ∈ (1, ∞] and complement the arguments of <i>q</i>-ratio CMSV from a geometrical view.","DOI":"10.1016/j.sigpro.2019.07.003","ScopusId":"2-s2.0-85068560059","NBN":"urn:nbn:se:umu:diva-161379","volume":"165","page":"128-132","container-title":"Signal Processing","ISSN":"1872-7557","keyword":"Sparse recovery; q-ratio sparsity; q-ratio constrained minimal singular values; ℓ1-truncated set q-width","publisher":"Elsevier","published":[{"raw":"2019-07-03T09:48:00.000+02:00"}],"created":[{"raw":"2019-07-03T09:48:34.434+02:00"}],"updated":[{"raw":"2023-03-24T10:59:18.407+01:00"}],"URL":"https://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-161379"},{"id":"diva2:1348429","type":"manuscript","issued":{"date-parts":[[2019]]},"title":"Statistical inference for block sparsity of complex signals","language":"eng","author":[{"family":"Wang","given":"Jianfeng","ORCID":"0000-0002-9341-1137","localId":"jiwa0016","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]},{"family":"Zhou","given":"Zhiyong","localId":"zhzh0022","affiliation":[{"name":"Department of Statistics, Zhejiang University City College, China"},{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]},{"family":"Yu","given":"Jun","ORCID":"0000-0001-5673-620X","localId":"juyu0002","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]}],"abstract":"Block sparsity is an important parameter in many algorithms to successfully recover block sparse signals under the framework of compressive sensing. However, it is often unknown and needs to beestimated. Recently there emerges a few research work about how to estimate block sparsity of real-valued signals, while there is, to the best of our knowledge, no investigation that has been conductedfor complex-valued signals. In this paper, we propose a new method to estimate the block sparsity of complex-valued signal. Its statistical properties are obtained and verified by simulations. In addition,we demonstrate the importance of accurately estimating the block sparsity in signal recovery through asensitivity analysis.","NBN":"urn:nbn:se:umu:diva-162998","keyword":"Block sparsity; Complex-valued signals; Multivariate isotropic symmetric α-stable distribution","published":[{"raw":"2019-09-04T11:57:00.000+02:00"}],"created":[{"raw":"2019-09-04T11:57:41.747+02:00"}],"updated":[{"raw":"2021-10-19T16:07:04.896+02:00"}],"URL":"https://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-162998"},{"id":"diva2:1834757","type":"manuscript","title":"Compressed sensing for low-count positron emission tomography denoising in measurement space","language":"eng","author":[{"family":"Leffler","given":"Klara","ORCID":"0000-0002-5130-1941","localId":"klle0001","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]},{"family":"Häggström","given":"Ida","affiliation":[{"name":"Department of Electrical Engineering, Chalmers University of Technology, Gothenburg, Sweden"}]},{"family":"Yu","given":"Jun","ORCID":"0000-0001-5673-620X","localId":"juyu0002","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]}],"NBN":"urn:nbn:se:umu:diva-220508","keyword":"compressed sensing; denoising; positron emission tomography","published":[{"raw":"2024-02-05T15:18:10.026+01:00"}],"created":[{"raw":"2024-02-05T15:18:10.098+01:00"}],"updated":[{"raw":"2025-02-09T05:20:24.842+01:00"}],"URL":"https://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-220508"},{"id":"diva2:1088704","type":"manuscript","title":"Contrast Agent Quantification by Using Spatial Information in Dynamic Contrast Enhanced MRI","language":"eng","author":[{"family":"Wang","given":"Jianfeng","ORCID":"0000-0002-9341-1137","localId":"jiwa0016","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]},{"family":"Garpebring","given":"Anders","ORCID":"0000-0002-0532-232X","localId":"anga0014","affiliation":[{"id":"779","name":"Umeå universitet, Radiofysik"}]},{"family":"Brynolfsson","given":"Patrik","localId":"pakbon02","affiliation":[{"id":"779","name":"Umeå universitet, Radiofysik"}]},{"family":"Liu","given":"Xijia","localId":"xili0017","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]},{"family":"Yu","given":"Jun","ORCID":"0000-0001-5673-620X","localId":"juyu0002","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]}],"abstract":"The purpose of this study is to investigate a method, using simulations, to improve contrast agent quantification in Dynamic Contrast Enhanced MRI. Bayesian hierarchical models (BHMs) are applied to smaller images (10×10×10) such that spatial information can be incorporated. Then exploratory analysis is done for larger images (64×64×64) by using maximum a posteriori (MAP).For smaller images: the estimators of proposed BHMs show improvements in terms of the root mean squared error compared to the estimators in existing method for a noise level equivalent of a 12-channel head coil at 3T. Moreover, Leroux model outperforms Besag models. For larger images: MAP estimators also show improvements by assigning Leroux prior.","NBN":"urn:nbn:se:umu:diva-133609","keyword":"Contrast agent quantification; BHM; Besag; Leroux; INLA; MAP","published":[{"raw":"2017-04-13T15:52:00.000+02:00"}],"created":[{"raw":"2017-04-13T15:52:35.098+02:00"}],"updated":[{"raw":"2023-09-14T17:19:41.630+02:00"}],"URL":"https://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-133609"},{"id":"diva2:1834756","type":"manuscript","title":"Filling of incomplete sinograms from sparse PET detector configurations using a residual U-Net","language":"eng","author":[{"family":"Leffler","given":"Klara","ORCID":"0000-0002-5130-1941","localId":"klle0001","affiliation":[{"id":"869","name":"Umeå universitet, Institutionen för matematik och matematisk statistik"}]},{"family":"Tommaso Luppino","given":"Luigi","affiliation":[{"name":"Department Physics and Technology, UiT The Arctic University of Norway, Tromsø, Norway"}]},{"family":"Kuttner","given":"Samuel","ORCID":"0000-0001-7747-9003","affiliation":[{"name":"University Hospital of North Norway, Tromsø, Norway; Physics and Technology, UiT The Arctic University of Norway, Tromsø, Norway; Department of Clinical Medicine, UiT The Arctic University of Norway, Tromsø, Norway"}]},{"family":"Söderkvist","given":"Karin","ORCID":"0000-0002-3683-3763","localId":"kansom97","affiliation":[{"id":"889252","name":"Umeå universitet, Institutionen för diagnostik och intervention"}]},{"family":"Axelsson","given":"Jan","ORCID":"0000-0002-3731-3612","localId":"jaax0004","affiliation":[{"id":"889252","name":"Umeå universitet, Institutionen för diagnostik och intervention"}]}],"NBN":"urn:nbn:se:umu:diva-220510","keyword":"positron emission tomography (PET); sparse PET; deep learning - artificial intelligence; residual U-net; gap filling; long axial field of view PET; total body PET","published":[{"raw":"2024-02-05T15:17:33.088+01:00"}],"created":[{"raw":"2024-02-05T15:17:33.161+01:00"}],"updated":[{"raw":"2025-02-09T05:20:26.341+01:00"}],"URL":"https://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-220510"}],"links":[{"type":"pid","link":"https://umu.diva-portal.org/smash/api/project/swecris/project:1299"}]}]