Abstract
We study the problem of deconvolution for light-sheet microscopy, where the data is corrupted by spatially varying blur and a combination of Poisson and Gaussian noise. The spatial variation of the point spread function of a light-sheet microscope is determined by the interaction between the excitation sheet and the detection objective PSF. We introduce a model of the image formation process that incorporates this interaction and we formulate a variational model that accounts for the combination of Poisson and Gaussian noise through a data fidelity term consisting of the infimal convolution of the single noise fidelities, first introduced in L. Calatroni et al. (SIAM J Imaging Sci 10(3):1196–1233, 2017). We establish convergence rates and a discrepancy principle for the infimal convolution fidelity and the inverse problem is solved by applying the primal–dual hybrid gradient (PDHG) algorithm in a novel way. Numerical experiments performed on simulated and real data show superior reconstruction results in comparison with other methods.
| Original language | English |
|---|---|
| Pages (from-to) | 968-992 |
| Number of pages | 25 |
| Journal | Journal of Mathematical Imaging and Vision |
| Volume | 64 |
| Early online date | 14 Jun 2022 |
| DOIs | |
| Publication status | Published - 30 Nov 2022 |
Bibliographical note
Funding Information:BT and LM gratefully acknowledge the funding by Isaac Newton Trust/Wellcome Trust ISSF/University of Cambridge Joint Research Grants Scheme and EPSRC EP/R025398/1. MOL and LM also thank the Gatsby Charitable Foundation for financial support. YK acknowledges financial support of the EPSRC (Fellowship EP/V003615/1), the Cantab Capital Institute for the Mathematics of Information at the University of Cambridge and the National Physical Laboratory. CBS acknowledges support from the Philip Leverhulme Prize, the Royal Society Wolfson Fellowship, the EPSRC Grants EP/S026045/1 and EP/T003553/1, EP/N014588/1, EP/T017961/1, the Wellcome Innovator Award RG98755, the Leverhulme Trust project Unveiling the invisible, the European Union Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 777826 NoMADS, the Cantab Capital Institute for the Mathematics of Information and the Alan Turing Institute. Imaging was performed at the Microscopy Facility of the Sainsbury Laboratory Cambridge University. We thank Dr. Alessandra Bonfanti and Dr. Sarah Robinson for providing the Marchantia sample and Prof. Sebastian Schornack and Dr. Giulia Arsuffi (Sainsbury Laboratory Cambridge University) for provision of the line of Marchantia used. We also acknowledge the support of NVIDIA Corporation with the donation of two Quadro P6000, a Tesla K40c and a Titan Xp GPU used for this research. For the purpose of open access, the authors have applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising.
Funding Information:
BT and LM gratefully acknowledge the funding by Isaac Newton Trust/Wellcome Trust ISSF/University of Cambridge Joint Research Grants Scheme and EPSRC EP/R025398/1. MOL and LM also thank the Gatsby Charitable Foundation for financial support. YK acknowledges financial support of the EPSRC (Fellowship EP/V003615/1), the Cantab Capital Institute for the Mathematics of Information at the University of Cambridge and the National Physical Laboratory. CBS acknowledges support from the Philip Leverhulme Prize, the Royal Society Wolfson Fellowship, the EPSRC Grants EP/S026045/1 and EP/T003553/1, EP/N014588/1, EP/T017961/1, the Wellcome Innovator Award RG98755, the Leverhulme Trust project Unveiling the invisible, the European Union Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 777826 NoMADS, the Cantab Capital Institute for the Mathematics of Information and the Alan Turing Institute. Imaging was performed at the Microscopy Facility of the Sainsbury Laboratory Cambridge University. We thank Dr. Alessandra Bonfanti and Dr. Sarah Robinson for providing the Marchantia sample and Prof. Sebastian Schornack and Dr. Giulia Arsuffi (Sainsbury Laboratory Cambridge University) for provision of the line of Marchantia used. We also acknowledge the support of NVIDIA Corporation with the donation of two Quadro P6000, a Tesla K40c and a Titan Xp GPU used for this research. For the purpose of open access, the authors have applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising.
Funding
BT and LM gratefully acknowledge the funding by Isaac Newton Trust/Wellcome Trust ISSF/University of Cambridge Joint Research Grants Scheme and EPSRC EP/R025398/1. MOL and LM also thank the Gatsby Charitable Foundation for financial support. YK acknowledges financial support of the EPSRC (Fellowship EP/V003615/1), the Cantab Capital Institute for the Mathematics of Information at the University of Cambridge and the National Physical Laboratory. CBS acknowledges support from the Philip Leverhulme Prize, the Royal Society Wolfson Fellowship, the EPSRC Grants EP/S026045/1 and EP/T003553/1, EP/N014588/1, EP/T017961/1, the Wellcome Innovator Award RG98755, the Leverhulme Trust project Unveiling the invisible, the European Union Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 777826 NoMADS, the Cantab Capital Institute for the Mathematics of Information and the Alan Turing Institute. Imaging was performed at the Microscopy Facility of the Sainsbury Laboratory Cambridge University. We thank Dr. Alessandra Bonfanti and Dr. Sarah Robinson for providing the Marchantia sample and Prof. Sebastian Schornack and Dr. Giulia Arsuffi (Sainsbury Laboratory Cambridge University) for provision of the line of Marchantia used. We also acknowledge the support of NVIDIA Corporation with the donation of two Quadro P6000, a Tesla K40c and a Titan Xp GPU used for this research. For the purpose of open access, the authors have applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising. BT and LM gratefully acknowledge the funding by Isaac Newton Trust/Wellcome Trust ISSF/University of Cambridge Joint Research Grants Scheme and EPSRC EP/R025398/1. MOL and LM also thank the Gatsby Charitable Foundation for financial support. YK acknowledges financial support of the EPSRC (Fellowship EP/V003615/1), the Cantab Capital Institute for the Mathematics of Information at the University of Cambridge and the National Physical Laboratory. CBS acknowledges support from the Philip Leverhulme Prize, the Royal Society Wolfson Fellowship, the EPSRC Grants EP/S026045/1 and EP/T003553/1, EP/N014588/1, EP/T017961/1, the Wellcome Innovator Award RG98755, the Leverhulme Trust project Unveiling the invisible, the European Union Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 777826 NoMADS, the Cantab Capital Institute for the Mathematics of Information and the Alan Turing Institute. Imaging was performed at the Microscopy Facility of the Sainsbury Laboratory Cambridge University. We thank Dr. Alessandra Bonfanti and Dr. Sarah Robinson for providing the Marchantia sample and Prof. Sebastian Schornack and Dr. Giulia Arsuffi (Sainsbury Laboratory Cambridge University) for provision of the line of Marchantia used. We also acknowledge the support of NVIDIA Corporation with the donation of two Quadro P6000, a Tesla K40c and a Titan Xp GPU used for this research. For the purpose of open access, the authors have applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising.
Keywords
- Deconvolution
- Light-sheet microscopy
- Numerical methods
- Poisson and Gaussian noise
- Primal–dual hybrid gradient
ASJC Scopus subject areas
- Statistics and Probability
- Modelling and Simulation
- Condensed Matter Physics
- Computer Vision and Pattern Recognition
- Geometry and Topology
- Applied Mathematics