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Compressive Phase Retrieval: Optimal Sample Complexity with Deep Generative Priors [article]

Paul Hand, Oscar Leong, Vladislav Voroninski
2020 arXiv   pre-print
In particular, tractable algorithms for compressive phase retrieval with sparsity priors have not been able to achieve optimal sample complexity.  ...  This has created an open problem in compressive phase retrieval: under generic, phaseless linear measurements, are there tractable reconstruction algorithms that succeed with optimal sample complexity?  ...  Lastly, we note that this result for compressive phase retrieval under optimal sample complexity implies recovery for linear compressive sensing under optimal sample complexity.  ... 
arXiv:2008.10579v1 fatcat:hx4xe3ie2jeg5gzmzxboyrm6nm

Robust Compressive Phase Retrieval via Deep Generative Priors [article]

Fahad Shamshad, Ali Ahmed
2018 arXiv   pre-print
This paper proposes a new framework to regularize the highly ill-posed and non-linear phase retrieval problem through deep generative priors using simple gradient descent algorithm.  ...  We demonstrate that proposed approach achieves impressive results when compared with traditional hand engineered priors including sparsity and denoising frameworks for number of measurements and robustness  ...  We show through extensive experiments that solving compressive phase retrieval problem using deep generative priors results in comparable performance to traditional prior based approaches with far fewer  ... 
arXiv:1808.05854v1 fatcat:bu3lhhrbqvgc7lddonj6b6foqq

Towards Sample-Optimal Compressive Phase Retrieval with Sparse and Generative Priors [article]

Zhaoqiang Liu, Subhroshekhar Ghosh, Jonathan Scarlett
2021 arXiv   pre-print
In this paper, motivated by recent advances in deep generative models, we provide recovery guarantees with near-optimal sample complexity for phase retrieval with generative priors.  ...  Compressive phase retrieval is a popular variant of the standard compressive sensing problem in which the measurements only contain magnitude information.  ...  No. of measurements m; s = 10 Supplementary Material Towards Sample-Optimal Compressive Phase Retrieval with Sparse and Generative Priors (NeurIPS 2021) Zhaoqiang Liu, Subhroshekhar Ghosh, and Jonathan  ... 
arXiv:2106.15358v2 fatcat:sgb4ii6olndxxl4dmvmpuzihte

Using Black-box Compression Algorithms for Phase Retrieval [article]

Milad Bakhshizadeh, Arian Maleki, Shirin Jalali
2020 arXiv   pre-print
First, COmpressive PhasE Retrieval (COPER) optimization, a computationally-intensive compression-based phase retrieval method, is proposed.  ...  Compressive phase retrieval refers to the problem of recovering a structured n-dimensional complex-valued vector from its phase-less under-determined linear measurements.  ...  Finally, [32] uses a deep generative network to model images and then uses the learned model as a prior to help the phase retrieval recovery algorithms.  ... 
arXiv:1712.03278v3 fatcat:rbxh65xepffjzfhxpoyqvbldfi

Joint neural phase retrieval and compression for energy- and computation-efficient holography on the edge

Yujie Wang, Praneeth Chakravarthula, Qi Sun, Baoquan Chen
2022 ACM Transactions on Graphics  
In this work, by distributing the computation and optimizing the transmission, we propose the first framework that jointly generates and compresses high-quality phase-only holograms.  ...  With our framework, we observed a reduction of 76% computation and consequently 83% in energy cost on edge devices, compared to the existing hologram generation methods.  ...  phase encoder 𝐸 𝑝 , a hyper-prior encoder 𝐸 ℎ , a hyper-prior decoder 𝐷 ℎ and a phase decoder 𝐷 𝑝 .  ... 
doi:10.1145/3528223.3530070 fatcat:c4vveakulvd3box5eezzgk5lt4

DeepInit Phase Retrieval [article]

Martin Reiche, Peter Jung
2020 arXiv   pre-print
We therefore propose DeepInit Phase Retrieval, which uses regularized gradient descent under a deep generative data prior to compute a trained initialization for a fast classical algorithm (e.g. the randomized  ...  This paper shows how data-driven deep generative models can be utilized to solve challenging phase retrieval problems, in which one wants to reconstruct a signal from only few intensity measurements.  ...  DeepInit Phase Retrieval also incorporates signal domain information using deep generative priors but does not suffer from reconstruction quality degradation caused by generator model error.  ... 
arXiv:2007.08214v1 fatcat:clz6ec525ja55h5yjlfzmjujcq

Deep Learning-based Compression for Phase-only Hologram

Hyunsuk Ko, Hui Yong Kim
2021 IEEE Access  
INDEX TERMS Computed-generated Hologram (CGH), Digital holography, deep learning-based compression, phase-only hologram.  ...  In this work, we propose a deep-learning based image compression network for phase-only holograms.  ...  ACKNOWLEDGMENT We thank ETRI (Electronics and Telecommunications Research Institute) for kindly providing us the phase-only CGH database.  ... 
doi:10.1109/access.2021.3084800 fatcat:zw3uavysfffh5pp5cxgfrebs3u

Non-Convex Structured Phase Retrieval [article]

Namrata Vaswani
2020 arXiv   pre-print
This article describes this work, with a focus on non-convex approaches that come with sample complexity guarantees under simple assumptions.  ...  Phase retrieval (PR), also sometimes referred to as quadratic sensing, is a problem that occurs in numerous signal and image acquisition domains ranging from optics, X-ray crystallography, Fourier ptychography  ...  prior: A recent work assumed a deep neural network based "generative prior" on the signal x * [36] .  ... 
arXiv:2006.13298v1 fatcat:yhnmdlsbkbgfxhzqugai3wlz7i

Class-Specific Blind Deconvolutional Phase Retrieval Under a Generative Prior [article]

Fahad Shamshad, Ali Ahmed
2020 arXiv   pre-print
We propose to solve this inverse problem using alternating gradient descent algorithm under two pretrained deep generative networks as priors; one is trained on sharp images and the other on blur kernels  ...  The proposed recovery algorithm strives to find a sharp image and a blur kernel in the range of the respective pre-generators that best explain the forward measurement model.  ...  Recently, pre-trained generative models have also shown remarkable performance for solving other inverse imaging problems including compressed sensing [16] , Fourier ptychography [26, 17] , phase retrieval  ... 
arXiv:2002.12578v1 fatcat:p3ioca5zxzfe3o5zdfskc3thvy

Signal retrieval with measurement system knowledge using variational generative model [article]

Zheyuan Zhu, Yangyang Sun, Johnathon White, Zenghu Chang, Shuo Pang
2019 arXiv   pre-print
Because most of the indirect measurement processes are well-described by physical models, signal retrieval can be solved with an iterative optimization that enforces measurement consistency and prior knowledge  ...  the measurement with high fidelity in a variety of linear and nonlinear ill-posed systems, including ultrafast pulse retrieval, coded aperture compressive video sensing and image retrieval from Fresnel  ...  The number on the compressed measurement indicates the fidelity of the measurement calculated from 4 retrieved frames.performed iterative maximum-a-posteriori reconstructions with TV prior and deep pixel-level  ... 
arXiv:1909.04188v1 fatcat:sqiob7h2hvezppgf7q6ui5auzy

Optimizing Intermediate Representations of Generative Models for Phase Retrieval [article]

Tobias Uelwer, Sebastian Konietzny, Stefan Harmeling
2022 arXiv   pre-print
To reduce this representation error in the context of phase retrieval, we first leverage a novel variation of intermediate layer optimization (ILO) to extend the range of the generator while still producing  ...  With extensive experiments on Fourier and Gaussian phase retrieval problems and thorough ablation studies, we can show the benefits of our modified ILO and the new initialization schemes.  ...  Generative priors for compressive phase retrieval have been analyzed by Hand et al. [14] and Liu et al. [15] .  ... 
arXiv:2205.15617v1 fatcat:dygk4bz5svcb5ppyj5kpn5ontu

Deep S^3PR: Simultaneous Source Separation and Phase Retrieval Using Deep Generative Models [article]

Christopher A. Metzler, Gordon Wetzstein
2020 arXiv   pre-print
This paper introduces and solves the simultaneous source separation and phase retrieval (S^3PR) problem.  ...  In this work, we demonstrate that by restricting the solutions to lie in the range of a deep generative model, we can constrain the search space sufficiently to solve S^3PR.  ...  Phase retrieval PR with generative models was introduced in (Hand et al., 2018) and .  ... 
arXiv:2002.05856v2 fatcat:xypgkqeilnhktoj26fdknbwt2u

Phase Retrieval Under a Generative Prior [article]

Paul Hand, Oscar Leong, Vladislav Voroninski
2018 arXiv   pre-print
optimal sample complexity.  ...  We corroborate these results with experiments showing that exploiting generative models in phase retrieval tasks outperforms sparse phase retrieval methods.  ...  The success of leveraging generative priors in compressed sensing along with the sample complexity bottlenecks in sparse phase retrieval have influenced this work to consider enforcing a generative prior  ... 
arXiv:1807.04261v1 fatcat:r7nkdt3b6vcxnnezktsrynjgo4

prDeep: Robust Phase Retrieval with a Flexible Deep Network [article]

Christopher A. Metzler, Philip Schniter, Ashok Veeraraghavan, Richard G. Baraniuk
2018 arXiv   pre-print
Unfortunately, traditional phase retrieval algorithms struggle in the presence of noise.  ...  Phase retrieval algorithms have become an important component in many modern computational imaging systems.  ...  By integrating a neural network into a traditional optimization algorithm, prDeep inherits the strengths of both optimization and deep-learning.  ... 
arXiv:1803.00212v2 fatcat:h6lshb7lvncafeoscgwgth7xqu

Learning Illumination Patterns for Coded Diffraction Phase Retrieval [article]

Zikui Cai, Rakib Hyder, M. Salman Asif
2020 arXiv   pre-print
We represent the phase retrieval method as an unrolled network with a fixed number of layers and minimize the recovery error by optimizing over the measurement parameters.  ...  In particular, we learn illumination patterns to recover signals from coded diffraction patterns using a fixed-cost alternating minimization-based phase retrieval method.  ...  Data-Driven Approaches for Phase Retrieval: A number of papers have recently explored the idea of replacing the classical (hand-designed) signal priors with deep generative priors for solving inverse problems  ... 
arXiv:2006.04199v1 fatcat:ypgrcdnyqjbfxaqranntka6wca
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