Noise amplification and ill-convergence of Richardson-Lucy deconvolution
Abstract Richardson-Lucy (RL) deconvolution optimizes the likelihood of the object estimate for an incoherent imaging system. It can offer an increase in contrast, but converges poorly, and shows enhancement of noise as the iteration progresses. We have discovered the underlying reason for this prob...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2025-01-01
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| Series: | Nature Communications |
| Online Access: | https://doi.org/10.1038/s41467-025-56241-x |
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| _version_ | 1832585559312171008 |
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| author | Yiming Liu Spozmai Panezai Yutong Wang Sjoerd Stallinga |
| author_facet | Yiming Liu Spozmai Panezai Yutong Wang Sjoerd Stallinga |
| author_sort | Yiming Liu |
| collection | DOAJ |
| description | Abstract Richardson-Lucy (RL) deconvolution optimizes the likelihood of the object estimate for an incoherent imaging system. It can offer an increase in contrast, but converges poorly, and shows enhancement of noise as the iteration progresses. We have discovered the underlying reason for this problematic convergence behaviour using a Cramér Rao Lower Bound (CRLB) analysis. An analytical expression for the CRLB diverges for spatial frequency components that approach the diffraction limit from below. The resulting mean noise variance per pixel diverges for large images. These results imply that a regular optimum of the likelihood does not exist, and that RL deconvolution is necessarily ill-convergent. |
| format | Article |
| id | doaj-art-40cf5b339a714090a3a0cb60d2f1a59c |
| institution | Kabale University |
| issn | 2041-1723 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Nature Communications |
| spelling | doaj-art-40cf5b339a714090a3a0cb60d2f1a59c2025-01-26T12:40:54ZengNature PortfolioNature Communications2041-17232025-01-011611810.1038/s41467-025-56241-xNoise amplification and ill-convergence of Richardson-Lucy deconvolutionYiming Liu0Spozmai Panezai1Yutong Wang2Sjoerd Stallinga3Department of Imaging Physics, Delft University of TechnologyDepartment of Imaging Physics, Delft University of TechnologyDepartment of Imaging Physics, Delft University of TechnologyDepartment of Imaging Physics, Delft University of TechnologyAbstract Richardson-Lucy (RL) deconvolution optimizes the likelihood of the object estimate for an incoherent imaging system. It can offer an increase in contrast, but converges poorly, and shows enhancement of noise as the iteration progresses. We have discovered the underlying reason for this problematic convergence behaviour using a Cramér Rao Lower Bound (CRLB) analysis. An analytical expression for the CRLB diverges for spatial frequency components that approach the diffraction limit from below. The resulting mean noise variance per pixel diverges for large images. These results imply that a regular optimum of the likelihood does not exist, and that RL deconvolution is necessarily ill-convergent.https://doi.org/10.1038/s41467-025-56241-x |
| spellingShingle | Yiming Liu Spozmai Panezai Yutong Wang Sjoerd Stallinga Noise amplification and ill-convergence of Richardson-Lucy deconvolution Nature Communications |
| title | Noise amplification and ill-convergence of Richardson-Lucy deconvolution |
| title_full | Noise amplification and ill-convergence of Richardson-Lucy deconvolution |
| title_fullStr | Noise amplification and ill-convergence of Richardson-Lucy deconvolution |
| title_full_unstemmed | Noise amplification and ill-convergence of Richardson-Lucy deconvolution |
| title_short | Noise amplification and ill-convergence of Richardson-Lucy deconvolution |
| title_sort | noise amplification and ill convergence of richardson lucy deconvolution |
| url | https://doi.org/10.1038/s41467-025-56241-x |
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