Inverse problem approaches for image reconstruction can improve resolution recovery over spatial filtering methods while reducing interference artifacts in digital off-axis holography. Prior works implemented explicit regularization operators in the image space and were only able to match intensity measurements approximatively. As a consequence, convergence to a strictly compatible solution was not possible. In this paper, we replace the non-convex image recon- struction problem for a sequence of surrogate convex problems. An iterative numerical solver is designed using a simple projection operator in the data domain and a Nesterov acceleration of the simultaneous Kaczmarz method. For regularization, the complex-valued object wavefield image is represented in the multiresolution CDF 9/7 wavelet domain and an energy-weighted preconditioning promotes minimum-norm solutions. Experiments demonstrate improved resolu- tion recovery and reduced spurious artifacts in reconstructed images. Furthermore, the method is resilient to additive Gaussian noise and subsampling of intensity measurements.
Schretter, C, Blinder, D, Bettens, S, Ottevaere, H & Schelkens, P 2017, 'Regularized non-convex image reconstruction in digital holographic microscopy', Optics Express, vol. 25, no. 14, pp. 16491-16508. https://doi.org/10.1364/OE.25.016491
Schretter, C., Blinder, D., Bettens, S., Ottevaere, H., & Schelkens, P. (2017). Regularized non-convex image reconstruction in digital holographic microscopy. Optics Express, 25(14), 16491-16508. https://doi.org/10.1364/OE.25.016491
@article{0bbf870d73e04af9b820dc5930a09c7f,
title = "Regularized non-convex image reconstruction in digital holographic microscopy",
abstract = "Inverse problem approaches for image reconstruction can improve resolution recovery over spatial filtering methods while reducing interference artifacts in digital off-axis holography. Prior works implemented explicit regularization operators in the image space and were only able to match intensity measurements approximatively. As a consequence, convergence to a strictly compatible solution was not possible. In this paper, we replace the non-convex image recon- struction problem for a sequence of surrogate convex problems. An iterative numerical solver is designed using a simple projection operator in the data domain and a Nesterov acceleration of the simultaneous Kaczmarz method. For regularization, the complex-valued object wavefield image is represented in the multiresolution CDF 9/7 wavelet domain and an energy-weighted preconditioning promotes minimum-norm solutions. Experiments demonstrate improved resolu- tion recovery and reduced spurious artifacts in reconstructed images. Furthermore, the method is resilient to additive Gaussian noise and subsampling of intensity measurements.",
keywords = "holography, image reconstruction, regularization, digital holography, microscopy",
author = "Colas Schretter and David Blinder and Stijn Bettens and Heidi Ottevaere and Peter Schelkens",
note = "Colas Schretter, David Blinder, Stijn Bettens, Heidi Ottevaere, and Peter Schelkens, {"}Regularized non-convex image reconstruction in digital holographic microscopy,{"} Opt. Express 25, 16491-16508 (2017)",
year = "2017",
month = jul,
day = "10",
doi = "10.1364/OE.25.016491",
language = "English",
volume = "25",
pages = "16491--16508",
journal = "Optics Express",
issn = "1094-4087",
publisher = "The Optical Society",
number = "14",
}