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Dadras, A., Leffler, K. & Yu, J. (2024). A ridgelet approach to poisson denoising.
Open this publication in new window or tab >>A ridgelet approach to poisson denoising
2024 (English)Manuscript (preprint) (Other academic)
Abstract [en]

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.

Keywords
sparse signal processing, compressed sensing, positron emission tomography, denoising, inpainting
National Category
Probability Theory and Statistics Signal Processing
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:umu:diva-220205 (URN)10.48550/arXiv.2401.16099 (DOI)978-91-8070-279-9 (ISBN)978-91-8070-280-5 (ISBN)
Funder
Swedish Research Council, 340-2013-5342
Available from: 2024-02-05 Created: 2024-02-05 Last updated: 2024-02-06Bibliographically approved
Leffler, K. (2024). The PET sampling puzzle: intelligent data sampling methods for positron emission tomography. (Doctoral dissertation). Umeå: Umeå University
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
Leffler, K., Häggström, I. & Yu, J. (2023). Compressed sensing for low-count PET denoising in measurement space. In: NORDSTAT 2023 Gothenburg: . Paper presented at The 29th Nordic Conference in Mathematical Statistics, Gothenburg, Sweden, June 19-22, 2023.. Göteborgs universitet
Open this publication in new window or tab >>Compressed sensing for low-count PET denoising in measurement space
2023 (English)In: NORDSTAT 2023 Gothenburg, Göteborgs universitet, 2023Conference paper, Poster (with or without abstract) (Refereed)
Abstract [en]

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.

Place, publisher, year, edition, pages
Göteborgs universitet, 2023
National Category
Probability Theory and Statistics Medical Image Processing Signal Processing
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:umu:diva-224907 (URN)
Conference
The 29th Nordic Conference in Mathematical Statistics, Gothenburg, Sweden, June 19-22, 2023.
Funder
Swedish Research Council, 340-2013-534
Available from: 2024-05-24 Created: 2024-05-24 Last updated: 2024-05-28Bibliographically approved
Leffler, K., Tommaso Luppino, L., Kuttner, S. & Axelsson, J. (2023). Deep learning-based filling of incomplete sinograms from low-cost, long axial field-of-view PET scanners with inter-detector gaps. In: The international networking symposiumon artificial intelligence and informatics in nuclear medicine: Program book. Paper presented at International Symposium on Artificial Intelligence and Informatics in Nuclear Medicine, Groningen, Netherlands, October 9-11, 2023. (pp. 59-59). University Medical Center Groningen
Open this publication in new window or tab >>Deep learning-based filling of incomplete sinograms from low-cost, long axial field-of-view PET scanners with inter-detector gaps
2023 (English)In: The international networking symposiumon artificial intelligence and informatics in nuclear medicine: Program book, University Medical Center Groningen , 2023, p. 59-59Conference paper, Oral presentation with published abstract (Refereed)
Place, publisher, year, edition, pages
University Medical Center Groningen, 2023
Keywords
positron emission tomography (PET), sparse PET, deep learning - artificial intelligence, residual U-net, gap filling, long axial field of view PET, total body PET
National Category
Medical Image Processing Computational Mathematics Computer Vision and Robotics (Autonomous Systems)
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:umu:diva-224909 (URN)
Conference
International Symposium on Artificial Intelligence and Informatics in Nuclear Medicine, Groningen, Netherlands, October 9-11, 2023.
Funder
Swedish Research Council, 340-2013-5342
Available from: 2024-05-24 Created: 2024-05-24 Last updated: 2024-05-29Bibliographically approved
Leffler, K., Zhou, Z. & Yu, J. (2020). An extended block restricted isometry property for sparse recovery with non-Gaussian noise. Journal of Computational Mathematics, 38(6), 827-838
Open this publication in new window or tab >>An extended block restricted isometry property for sparse recovery with non-Gaussian noise
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
Keywords
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:nbn:se:umu:diva-163366 (URN)10.4208/jcm.1905-m2018-0256 (DOI)000540835100001 ()2-s2.0-85092354908 (Scopus ID)
Funder
Swedish Research Council, 340-2013-5342
Available from: 2019-09-17 Created: 2019-09-17 Last updated: 2024-02-06Bibliographically 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: 2024-02-06Bibliographically approved
Leffler, K., Zhou, Z. & Yu, J. (2018). An Extended Block Restricted Isometry Property for Sparse Recovery with Non-Gaussian Noise. In: : . Paper presented at COMPSTAT 2018, Iasi, Romania, August 28-31, 2018.
Open this publication in new window or tab >>An Extended Block Restricted Isometry Property for Sparse Recovery with Non-Gaussian Noise
2018 (English)Conference paper, Poster (with or without abstract) (Refereed)
Abstract [en]

Recovering an unknown signal from significantly fewer measurements is a fundamental aspect in computational sciences today. The key ingredient is the sparsity of the unknown signal, a realisation that that has led to the theory of compressed censing, through which successful recovery of high dimensional (approximately) sparse signals is now possible at a rate significantly lower than the Nyquist sampling rate. Today, an interesting challenge lies in customizing the recovery process to take into account prior knowledge about e.g. signal structure and properties of present noise. We study recovery conditions for block sparse signal reconstruction from compressed measurements when partial support information is available via weighted mixed l2/lp minimization. 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. Thereby, we also establish a setting wherein we are not restricted to a Gaussian measurement noise. The results are illustrated with a series of numerical experiments.

Keywords
Compressive sensing, block restricted isometry property, sparse recovery, non-Gaussian noise
National Category
Probability Theory and Statistics Signal Processing Medical Image Processing
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:umu:diva-154629 (URN)
Conference
COMPSTAT 2018, Iasi, Romania, August 28-31, 2018
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: 2018-12-20 Created: 2018-12-20 Last updated: 2024-02-06Bibliographically approved
Leffler, K., Häggström, I. & Yu, J. (2018). Intelligent data sampling promotes accelerated medical imaging: sharper positron emission tomography. In: : . Paper presented at The 6th Swedish Workshop on Data Science (SweDS18), Umeå, Sweden, November 20-21, 2018.
Open this publication in new window or tab >>Intelligent data sampling promotes accelerated medical imaging: sharper positron emission tomography
2018 (English)Conference paper, Oral presentation with published abstract (Refereed)
National Category
Probability Theory and Statistics Medical Image Processing Signal Processing
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:umu:diva-154631 (URN)
Conference
The 6th Swedish Workshop on Data Science (SweDS18), Umeå, Sweden, November 20-21, 2018
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: 2018-12-20 Created: 2018-12-20 Last updated: 2024-02-06Bibliographically approved
Leffler, K., Häggström, I. & Yu, J.Compressed sensing for low-count positron emission tomography denoising in measurement space.
Open this publication in new window or tab >>Compressed sensing for low-count positron emission tomography denoising in measurement space
(English)Manuscript (preprint) (Other academic)
Keywords
compressed sensing, denoising, positron emission tomography
National Category
Signal Processing Computational Mathematics Medical Image Processing
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:umu:diva-220508 (URN)
Funder
Swedish Research Council, 340-2013-5342
Available from: 2024-02-05 Created: 2024-02-05 Last updated: 2024-02-06
Leffler, K., Tommaso Luppino, L., Kuttner, S., Söderkvist, K. & Axelsson, J.Filling of incomplete sinograms from sparse PET detector configurations using a residual U-Net.
Open this publication in new window or tab >>Filling of incomplete sinograms from sparse PET detector configurations using a residual U-Net
Show others...
(English)Manuscript (preprint) (Other academic)
Keywords
positron emission tomography (PET), sparse PET, deep learning - artificial intelligence, residual U-net, gap filling, long axial field of view PET, total body PET
National Category
Medical Image Processing Computational Mathematics Computer Vision and Robotics (Autonomous Systems)
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:umu:diva-220510 (URN)
Funder
Swedish Research Council, 340-2013-5342
Available from: 2024-02-05 Created: 2024-02-05 Last updated: 2024-02-06
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-5130-1941

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