GSURE criterion for unsupervised regularized reconstruction in tomographic diffractive microscopy

Abstract

We propose an unsupervised regularized inversion method for reconstruction of the 3D refractive index map of a sample in tomographic diffractive microscopy. It is based on the minimization of the generalized Stein’s unbiased risk estimator (GSURE) to automatically estimate optimal values for the hyperparameters of one or several regularization terms (sparsity, edge-preserving smoothness, total variation). We evaluate the performance of our approach on simulated and experimental limited-view data. Our results show that GSURE is an efficient criterion to find suitable regularization weights, which is a critical task, particularly in the context of reducing the amount of required data to allow faster yet efficient acquisitions and reconstructions.

Recent Advances and Current Trends in Transmission Tomographic Diffraction Microscopy

“…The calculation of the complex field at the next layer, , can be performed using the beam propagation method (BPM) [ 154 , 155 ], in paraxial version [ 142 , 148 , 156 ] or improved versions [ 150 , 157 ]: where is the illumination angle, is the layer thickness, F is the 2D Fourier transform, and is the refractive index contrast.…”

Multispectral in-line hologram reconstruction with aberration compensation applied to Gram-stained bacteria microscopy

“…The hyperparameters and can then be selected such that the reconstruction of the beads using the regularization be as close as the ground-truth obtained using model fitting. Accordingly, we propose an unsupervised method to tune these hyperparameters that consists in solving the following bi-level problem: Note that alternative unsupervised techniques, such as the Morozov’s discrepancy principle 46 , L-Curve 47 or the minimization of the Stein Unbiased Risk Estimator (SURE) 48 – 50 could also be considered to tune the regularization hyperparameters.…”