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Noise amplification and ill-convergence of Richardson-Lucy deconvolution

Author

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  • Yiming Liu

    (Delft University of Technology)

  • Spozmai Panezai

    (Delft University of Technology)

  • Yutong Wang

    (Delft University of Technology)

  • Sjoerd Stallinga

    (Delft University of Technology)

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.

Suggested Citation

  • Yiming Liu & Spozmai Panezai & Yutong Wang & Sjoerd Stallinga, 2025. "Noise amplification and ill-convergence of Richardson-Lucy deconvolution," Nature Communications, Nature, vol. 16(1), pages 1-8, December.
    • Handle: RePEc:nat:natcom:v:16:y:2025:i:1:d:10.1038_s41467-025-56241-x
    DOI: 10.1038/s41467-025-56241-x
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