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An extended block restricted isometry property for sparse recovery with non-Gaussian noise
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.ORCID iD: 0000-0002-5130-1941
Department of Statistics, Zhejiang University City College, China.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (Mathematical Statistics)ORCID iD: 0000-0001-5673-620X
2020 (English)In: Journal of Computational Mathematics, ISSN 0254-9409, E-ISSN 1991-7139, Vol. 38, no 6, p. 827-838Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Global Science Press, 2020. Vol. 38, no 6, p. 827-838
Keywords [en]
Compressed sensing, block sparsity, partial support information, signal reconstruction, convex optimization
National Category
Signal Processing Probability Theory and Statistics Computational Mathematics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:umu:diva-163366DOI: 10.4208/jcm.1905-m2018-0256ISI: 000540835100001Scopus ID: 2-s2.0-85092354908OAI: oai:DiVA.org:umu-163366DiVA, id: diva2:1351857
Part of project
Statistical modelling and intelligent data sampling in MRI and PET measurements for cancer therapy assessment, Swedish Research Council
Funder
Swedish Research Council, 340-2013-5342Available from: 2019-09-17 Created: 2019-09-17 Last updated: 2024-02-06Bibliographically approved
In thesis
1. The PET sampling puzzle: intelligent data sampling methods for positron emission tomography
Open this publication in new window or tab >>The PET sampling puzzle: intelligent data sampling methods for positron emission tomography
2024 (English)Doctoral thesis, comprehensive summary (Other academic)
Alternative title[sv]
PET-samplingspusslet : intelligenta datainsamlingsmetoder för positronemissionstomografi
Abstract [en]

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.

Place, publisher, year, edition, pages
Umeå: Umeå University, 2024. p. 30
Series
Research report in mathematical statistics, ISSN 1653-0829 ; 76/24
Keywords
sparse signal processing, compressed sensing, Poisson denoising, positron emission tomography (PET), sinogram denoising, sinogram inpainting, deep learning
National Category
Probability Theory and Statistics Signal Processing Medical Image Processing Computational Mathematics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:umu:diva-220515 (URN)9789180702799 (ISBN)9789180702805 (ISBN)
Public defence
2024-02-29, BIO.E 203 (Aula Biologica), Umeå, 09:00 (English)
Opponent
Supervisors
Funder
Swedish Research Council, 340-2013-5342
Available from: 2024-02-08 Created: 2024-02-05 Last updated: 2024-02-08Bibliographically approved

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Leffler, KlaraYu, Jun

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