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Regularized non-convex image reconstruction in digital holographic microscopy This publication appears in: Optics Express Authors: C. Schretter, D. Blinder, S. Bettens, H. Ottevaere and P. Schelkens Volume: 25 Issue: 14 Pages: 16491-16508 Publication Date: Jul. 2017
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.
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