# Phase Retrieval from Coded Diffraction Patterns

arXiv: https://arxiv.org/abs/1310.3240 · HTML: https://mlsanity.com/paper/1310.3240/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Oct 2013.

## Built on by (most cited first, 26 of 26)

- [Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors](https://mlsanity.com/paper/2405.18782/) (2024)
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- [Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach](https://mlsanity.com/paper/2506.03979/) (2025)
- [Randomly Initialized Alternating Least Squares: Fast Convergence for Matrix Sensing](https://mlsanity.com/paper/2204.11516/) (2022)
- [SiSPRNet: End-to-End Learning for Single-Shot Phase Retrieval](https://mlsanity.com/paper/2205.11434/) (2022)
- [Spectral Estimators for Structured Generalized Linear Models via Approximate Message Passing](https://mlsanity.com/paper/2308.14507/) (2023)
- [DOLPH: Diffusion Models for Phase Retrieval](https://mlsanity.com/paper/2211.00529/) (2022)
- [PRISTA-Net: Deep Iterative Shrinkage Thresholding Network for Coded Diffraction Patterns Phase Retrieval](https://mlsanity.com/paper/2309.04171/) (2023)
- [Total Least Squares Phase Retrieval](https://mlsanity.com/paper/2102.00927/) (2021)
- [Provable Phase Retrieval with Mirror Descent](https://mlsanity.com/paper/2210.09248/) (2022)
- [Fast and Robust Phase Retrieval via Deep Expectation-Consistent Approximation](https://mlsanity.com/paper/2407.09687/) (2024)
- [On Stochastic Variance Reduced Gradient Method for Semidefinite Optimization](https://mlsanity.com/paper/2101.00236/) (2021)
- [Provably Convergent Algorithms for Solving Inverse Problems Using Generative Models](https://mlsanity.com/paper/2105.06371/) (2021)
- [Coded Illumination for Improved Lensless Imaging](https://mlsanity.com/paper/2111.12862/) (2021)
- [Solving Inverse Problems using Diffusion with Iterative Colored Renoising](https://mlsanity.com/paper/2501.17468/) (2025)
- [Unfolding-Aided Bootstrapped Phase Retrieval in Optical Imaging](https://mlsanity.com/paper/2203.01695/) (2022)
- [Convex Augmentation for Total Variation Based Phase Retrieval](https://mlsanity.com/paper/2205.00834/) (2022)
- [Towards Practical Single-shot Phase Retrieval with Physics-Driven Deep Neural Network](https://mlsanity.com/paper/2208.08604/) (2022)
- [Single-shot Phase Retrieval from a Fractional Fourier Transform Perspective](https://mlsanity.com/paper/2311.10950/) (2023)
- [Phase transition of descending phase retrieval algorithms](https://mlsanity.com/paper/2506.18275/) (2025)
- [Optimal spectral initializers impact on phase retrieval phase transitions -- an RDT view](https://mlsanity.com/paper/2506.18279/) (2025)
- [Phase retrieval with rank d measurements -- descending algorithms phase transitions](https://mlsanity.com/paper/2506.18282/) (2025)
- [DLMMPR:Deep Learning-based Measurement Matrix for Phase Retrieval](https://mlsanity.com/paper/2511.12556/) (2025)
- [Pupil Design for Computational Wavefront Estimation](https://mlsanity.com/paper/2604.00225/) (2026)
- [Convex Basins in Single-Index Model Loss Landscapes: Applications to Robust Recovery under Strong Adversarial Corruption](https://mlsanity.com/paper/2605.29497/) (2026)

## Abstract (arXiv)

This paper considers the question of recovering the phase of an object from intensity-only measurements, a problem which naturally appears in X-ray crystallography and related disciplines. We study a physically realistic setup where one can modulate the signal of interest and then collect the intensity of its diffraction pattern, each modulation thereby producing a sort of coded diffraction pattern. We show that PhaseLift, a recent convex programming technique, recovers the phase information exactly from a number of random modulations, which is polylogarithmic in the number of unknowns. Numerical experiments with noiseless and noisy data complement our theoretical analysis and illustrate our approach.