Alternating Phase Projected Gradient Descent with Generative Priors for Solving Compressive Phase Retrieval

Hyder, Rakib; Shah, Viraj; Hegde, Chinmay; Asif, M. Salman

doi:10.1109/icassp.2019.8682811

Cited by 39 publications

(35 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We first consider synthetic experiments on a two-layer network given by G(z) = N (0, 1). And the dimension of latent vector k is chosen from [10,15,20,25,30]. We set the total number of iterations to T = 300, and the number of phaseless measurement m ranges from 20 to 1000 with interval 50.…”

Section: Results Of Random Target On Fully-connected Generatormentioning

confidence: 99%

“…The average results are displayed in Figure 10b,c. One can see that the presented method is of good robustness against noise and a good stability at SNR > 10 dB when intensity measurement m < n. Compared with the classical imaging technology, the proposed method cannot reconstruct the targets that are not in the range of a generative model G as in [25,26,30], and its reconstruction results under high intensity measurements are not as perfect as other methods. However, it can use the prior information provided by the generative model to achieve the high-resolution reconstruction of targets with different sparseness when the intensity measurement m < n, which greatly reduces the complexity of solving the target scattering coefficient and the difficulty of hardware required for the echo signal detection.…”

Section: Discussionmentioning

confidence: 99%

“…Motivated by the study of phase recovery problem under Gaussian measurements Ref. [25][26][27], we designed Deep-GD algorithm for PL-TCAI, and the processing framework of the algorithm is shown in Figure 2. One can clearly see that the framework is actually an intuitive application of the idea of deep generative network to PL-TCAI tasks.…”

Section: Imaging Algorithmmentioning

confidence: 99%

“…In multiple scattering media imaging and holography [23,24], the neural network can act as a general and powerful mapping function, and breakthroughs have been made in imaging time and quality. Moreover, there have been a number of advancements for phase recovery problem by leveraging the deep generative neural network [25][26][27], which is learned from massive amounts of train data. However, these researches mainly focus on the sparse Gaussian phase recovery problem, and they also do not consider the noise resistance and stability of the algorithm.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Phaseless Terahertz Coded-Aperture Imaging Based on Deep Generative Neural Network

et al. 2021

View full text Add to dashboard Cite

As a promising terahertz radar imaging technology, phaseless terahertz coded-aperture imaging (PL-TCAI) has many advantages such as simple system structure, forward-looking imaging and staring imaging and so forth. However, it is very difficult to recover a target only from its intensity measurements. Although some methods have been proposed to deal with this problem, they require a large number of intensity measurements for both sparse and extended target reconstruction. In this work, we propose a method for PL-TCAI by modeling target scattering coefficient as being in the range of a generative model. Theoretically, we analyze and model the system structure, derive the matrix imaging equation, and then study the deep phase retrieval algorithm. Numerical tests based on different generative models show that the targets with the different spareness can achieve high resolution reconstruction when the number of intensity measurements are smaller than the number of target grids. Also, we find that the proposed method has good anti-noise and stability.

show abstract

Section: Results Of Random Target On Fully-connected Generatormentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Imaging Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Phaseless Terahertz Coded-Aperture Imaging Based on Deep Generative Neural Network

et al. 2021

View full text Add to dashboard Cite

show abstract

“…In recent years, a number of iterative algorithms have been proposed for solving the problem in (2), which includes lifting-based convex methods, alternating minimization-based nonconvex methods, and greedy methods [6][7][8][9]. Our goal is to learn a set of illumination patterns to optimize the recovery of an alternating minimization (AltMin) algorithm for solving the problem in (2).…”

Section: Introductionmentioning

confidence: 99%

Data-Driven Illumination Patterns For Coded Diffraction Imaging

Cai

Hyder

Asif

2021

2021 IEEE International Conference on Image Processing (ICIP)

Self Cite

View full text Add to dashboard Cite

Signal recovery from nonlinear measurements involves solving an iterative optimization problem. In this paper, we present a framework to optimize the sensing parameters to improve the quality of the signal recovered by the given iterative method. In particular, we learn illumination patterns to recover signals from coded diffraction patterns using a fixed-cost alternating minimization-based phase retrieval method. Coded diffraction phase retrieval is a physically realistic system in which the signal is first modulated by a sequence of codes before the sensor records its Fourier amplitude. 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. Since the number of iterations/layers are fixed, the recovery runs under a fixed cost. We present extensive simulation results on a variety of datasets under different conditions and a comparison with existing methods. Our results demonstrate that the proposed method provides near-perfect reconstruction using patterns learned with a small number of training images. Our proposed method provides significant improvements over existing methods both in terms of accuracy and speed.

show abstract

Compressive phase retrieval: Optimal sample complexity with deep generative priors

Hand,

Leong,

Voroninski

2023

Comm Pure Appl Math

View full text Add to dashboard Cite

Advances in compressive sensing (CS) provided reconstruction algorithms of sparse signals from linear measurements with optimal sample complexity, but natural extensions of this methodology to nonlinear inverse problems have been met with potentially fundamental sample complexity bottlenecks. 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? Meanwhile, progress in machine learning has led to the development of new data‐driven signal priors in the form of generative models, which can outperform sparsity priors with significantly fewer measurements. In this work, we resolve the open problem in compressive phase retrieval and demonstrate that generative priors can lead to a fundamental advance by permitting optimal sample complexity by a tractable algorithm. We additionally provide empirics showing that exploiting generative priors in phase retrieval can significantly outperform sparsity priors. These results provide support for generative priors as a new paradigm for signal recovery in a variety of contexts, both empirically and theoretically. The strengths of this paradigm are that (1) generative priors can represent some classes of natural signals more concisely than sparsity priors, (2) generative priors allow for direct optimization over the natural signal manifold, which is intractable under sparsity priors, and (3) the resulting non‐convex optimization problems with generative priors can admit benign optimization landscapes at optimal sample complexity, perhaps surprisingly, even in cases of nonlinear measurements.

show abstract

Alternating Phase Projected Gradient Descent with Generative Priors for Solving Compressive Phase Retrieval

Cited by 39 publications

References 20 publications

Phaseless Terahertz Coded-Aperture Imaging Based on Deep Generative Neural Network

Phaseless Terahertz Coded-Aperture Imaging Based on Deep Generative Neural Network

Data-Driven Illumination Patterns For Coded Diffraction Imaging

Compressive phase retrieval: Optimal sample complexity with deep generative priors

Contact Info

Product

Resources

About