Sub-Diffraction Imaging Using Fourier Ptychography and Structured Sparsity

Jagatap, Gauri; Chen, Zhengyu; Hegde, Chinmay; Vaswani, Namrata

doi:10.1109/icassp.2018.8461302

Cited by 13 publications

(11 citation statements)

References 25 publications

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“…We consider IERA (Iterative Error Reduction Algorithm) [2] and CoPRAM [16] as baseline methods. IERA solves FP problem by alternatively enforcing spatial and Fourier domain constraints whereas Co-PRAM exploits the underlying sparse structure of true signal for faithful reconstruction at low subsampling ratios.…”

Section: Baseline Methodsmentioning

confidence: 99%

“…where A = M F −1 P • F is the measurement model prior to optical sensor acquisition step, • denotes the Hadamard product and M is the subsampling operator. Subsampling operator when applied to an image, randomly picks a fraction of samples (f ) discarding the others [16]. We define the subsampling ratio as the fraction of samples retained by M divided by the total number of observed samples i.e.…”

Section: Formulationmentioning

confidence: 99%

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Deep Ptych: Subsampled Fourier Ptychography Using Generative Priors

Shamshad

Abbas

Ahmed

2019

ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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This paper proposes a novel framework to regularize the highly ill-posed and non-linear Fourier ptychography problem using generative models. We demonstrate experimentally that our proposed algorithm, Deep Ptych, outperforms the existing Fourier ptychography techniques, in terms of quality of reconstruction and robustness against noise, using far fewer samples. We further modify the proposed approach to allow the generative model to explore solutions outside the range, leading to improved performance.

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Section: Baseline Methodsmentioning

confidence: 99%

Section: Formulationmentioning

confidence: 99%

Deep Ptych: Subsampled Fourier Ptychography Using Generative Priors

Shamshad

Abbas

Ahmed

2019

ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…The root-mean-squared measurements estimator is adopted instead of the spectral initialization. The experiments demonstrate that spectral initialization succeeds for Gaussian measurements [ 23 , 25 , 29 , 30 , 31 ], it fails for FP setup (See [ 32 ] for detail). This surprising behavior is also noted in the research [ 22 , 33 ].…”

Section: Methodsmentioning

confidence: 99%

Sub-Diffraction Visible Imaging Using Macroscopic Fourier Ptychography and Regularization by Denoising

Wen

Song

et al. 2018

Sensors

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Imaging past the diffraction limit is of significance to an optical system. Fourier ptychography (FP) is a novel coherent imaging technique that can achieve this goal and it is widely used in microscopic imaging. Most phase retrieval algorithms for FP reconstruction are based on Gaussian measurements which cannot extend straightforwardly to long range, sub-diffraction imaging setup because of laser speckle noise corruption. In this work, a new FP reconstruction framework is proposed for macroscopic visible imaging. When compared with existing research, the reweighted amplitude flow algorithm is adopted for better signal modeling, and the Regularization by Denoising (RED) scheme is introduced to reduce the effects of speckle. Experiments demonstrate that the proposed method can obtain state-of-the-art recovered results on both visual and quantitative metrics without increasing computation cost, and it is flexible for real imaging applications.

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“…For th camera of coherent array, the forward operator has the form of A = M F −1 P • F, where F denotes Fourier matrix, P is a pupil mask that acts as a bandpass filter in the Fourier domain, • represents Hadamard product, and M is subsampling operator. Subsampling operator when applied to measurements y, randomly picks a fraction of samples discarding the others [19]. We define the subsampling ratio as the fraction of samples The subsampling mask resembles the operation of a binary matrix having entries 1's and 0's.…”

Section: Subsampled Fp Modelmentioning

confidence: 99%

Class-Specific Blind Deconvolutional Phase Retrieval Under a Generative Prior

Shamshad¹,

Ahmed²

2020

Preprint

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In this paper, we consider the highly ill-posed problem of jointly recovering two real-valued signals from the phaseless measurements of their circular convolution. The problem arises in various imaging modalities such as Fourier ptychography, X-ray crystallography, and in visible light communication. 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. In doing so, we are able to reconstruct quality image estimates. Moreover, the numerics show that the proposed approach performs well on the challenging measurement models that reflect the physically realizable imaging systems and is also robust to noise.

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Sub-Diffraction Imaging Using Fourier Ptychography and Structured Sparsity

Cited by 13 publications

References 25 publications

Deep Ptych: Subsampled Fourier Ptychography Using Generative Priors

Deep Ptych: Subsampled Fourier Ptychography Using Generative Priors

Sub-Diffraction Visible Imaging Using Macroscopic Fourier Ptychography and Regularization by Denoising

Class-Specific Blind Deconvolutional Phase Retrieval Under a Generative Prior

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