Undersampled Phase Retrieval with Outliers

ADMM-inspired image reconstruction for terahertz off-axis digital holography

Image reconstruction in off-axis terahertz digital holography is complicated due to the harsh recording conditions and the non-convexity form of the problem. In this paper, we propose an inverse problem-based reconstruction technique that jointly reconstructs the object field and the amplitude of the reference field. Regularization in the wavelet domain promotes a sparse object solution. A single objective function combining the data-fidelity and regularization terms is optimized with a dedicated algorithm based on an alternating direction method of multipliers framework. Each iteration alternates between two consecutive optimizations using projections operating on each solution and one soft thresholding operator applying to the object solution. The method is preceded by a windowing process to alleviate artifacts due to the mismatch between camera frame truncation and periodic boundary conditions assumed to implement convolution operators. Experiments demonstrate the effectiveness of the proposed method, in particular, improvements of reconstruction quality, compared to two other methods.

A constrained method for lensless coherent imaging of thin samples

Lensless inline holography can produce high-resolution images over a large field of view (FoV). In a previous work [Appl. Opt.60, B38 (2021)APOPAI0003-693510.1364/AO.414976], we showed that (i) the actual FoV can be extrapolated outside of the camera FoV and (ii) the effective resolution of the setup can be several times higher than the resolution of the camera. In this paper, we present a reconstruction method to recover high resolution with an extrapolated FoV image of the phase and the amplitude of a sample from aliased intensity measurements taken at a lower resolution.

Proximity operators for phase retrieval

We present a new formulation of a family of proximity operators that generalize the projector step for phase retrieval. These proximity operators for noisy intensity measurements can replace the classical "noise-free" projection in any projection-based algorithm. They are derived from a maximum-likelihood formulation and admit closed form solutions for both the Gaussian and the Poisson cases. In addition, we extend these proximity operators to under-sampled intensity measurements. To assess their performance, these operators are exploited in a classical Gerchberg-Saxton algorithm. We present numerical experiments showing that the reconstructed complex amplitudes with these proximity operators always perform better than using the classical intensity projector, while their computational overhead is moderate.