Coded diffraction system in X-ray crystallography using a boolean phase coded aperture approximation

Pinilla, Samuel; Poveda, Juan Carlos; Argüello, Henry

doi:10.1016/j.optcom.2017.11.035

Cited by 15 publications

(13 citation statements)

References 15 publications

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“…This limits its use for large scale scenes because of the expensive computational memory requirements and the potential overfitting problems [64]. We propose to reduce the number of trainable parameters by adding spatial structure to each CA so that a kernel Q s of size ∆ n × ∆ m N × M is periodically repeated as follows Number of snapshots in (10) Trainable parameters in (14) manufacturing noise in (16) Conditionality in (13) Multishot correlation in (12) 4. Regularizer Fig.…”

Section: F Data Driven Conditionality Constraintmentioning

confidence: 99%

“…Analytically, the CA is modeled as a tensor array where each spatial location has a particular response to the incoming wavefront. According to the nature of the entry values they can be found polarizer CA [4], complex-modulating CA [10], phase CA [13], intensity-modulating CA [14], among others. This work focuses on CAs modulating the intensity through (i) binary CA (BCA) [15], with opaque and translucent elements that completely block or let pass the wavefront, and (ii) realvalued CA [16] that attenuates the wavefront at different levels.…”

Section: Introductionmentioning

confidence: 99%

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Deep Coded Aperture Design: An End-to-End Approach for Computational Imaging Tasks

Bacca¹,

Gelvez²,

Argüello³

2021

Preprint

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Covering from photography to depth and spectral estimation, diverse computational imaging (CI) applications benefit from the versatile modulation of coded apertures (CAs). The light wave fields as space, time, or spectral can be modulated to obtain projected encoded information at the sensor that is then decoded by efficient methods, such as the modern deep learning decoders. Despite the CA can be fabricated to produce an analog modulation, a binary CA is mostly preferred since easier calibration, higher speed, and lower storage are achieved. As the performance of the decoder mainly depends on the structure of the CA, several works optimize the CA ensembles by customizing regularizers for a particular application without considering critical physical constraints of the CAs. This work presents an end-to-end (E2E) deep learning-based optimization of CAs for CI tasks. The CA design method aims to cover a wide range of CI problems easily changing the loss function of the deep approach. The designed loss function includes regularizers to fulfill the widely used sensing requirements of the CI applications. Mainly, the regularizers can be selected to optimize the transmittance, the compression ratio and the correlation between measurements, while a binary CA solution is encouraged, and the performance of the CI task is maximized in applications such as restoration, classification, and semantic segmentation.

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Section: F Data Driven Conditionality Constraintmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Deep Coded Aperture Design: An End-to-End Approach for Computational Imaging Tasks

Bacca¹,

Gelvez²,

Argüello³

2021

Preprint

Self Cite

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“…where ℓ kt = ϕµ(|a H kt z|) − q kt 2 . Note that setting µ = 0 in (8) leads to the non-smooth problem in (3). Note also that recent works such as [9,15] have addressed the non-smoothness of g(z) in (4) by introducing truncation parameters into the gradient step in order to eliminate the errors in the estimated descent direction.…”

Section: Stochastic Smoothing Phase Retrieval Algorithmmentioning

confidence: 99%

“…Phase retrieval is an inverse problem that consists of recovering a signal from the squared modulus of some linear transforms, which has proved efficient in in various applications such as, optics [1], astronomy [2] and X-ray crystallography [3,4,5,6]. Recent works [7,8,9] have been proposed to solve the phase retrieval problem by optimizing a non-convex and non-smooth objective function with a gradient descent algorithm based on the Wirtinger derivative with an appropriate initialization.…”

Section: Introductionmentioning

confidence: 99%

A Smoothing Stochastic Phase Retrieval Algorithm for Solving Random Quadratic Systems

Pinilla

Bacca

Tourneret

et al. 2018

2018 IEEE Statistical Signal Processing Workshop (SSP)

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A novel Stochastic Smoothing Phase Retrieval (SSPR) algorithm is studied to reconstruct an unknown signal x ∈ R n or C n from a set of absolute square projections y k = | a k , x | 2. This inverse problem is known in the literature as Phase Retrieval (PR). Recent works have shown that the PR problem can be solved by optimizing a nonconvex and non-smooth cost function. Contrary to the recent truncated gradient descend methods developed to solve the PR problem (using truncation parameters to bypass the non-smoothness of the cost function), the proposed algorithm approximates the cost function of interest by a smooth function. Optimizing this smooth function involves a single equation per iteration, which leads to a simple scalable and fast method especially for large sample sizes. Extensive simulations suggest that SSPR requires a reduced number of measurements for recovering the signal x, when compared to recently developed stochastic algorithms. Our experiments also demonstrate that SSPR is robust to the presence of additive noise and has a speed of convergence comparable with that of state-of-the-art algorithms.

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“…In many applications of science and engineering, it is required to recover a signal from the squared modulus of any linear transform, which is known as phase retrieval (PR). Such a task is present in optics [1], astronomical imaging [2], microscopy [3] and x-ray crystallography [4,5,6], where the optical sensors measure the intensities of the reflection, but they are not able to measure the phase of the signal. For example, in x-ray crystallography [4], PR is used to determine the atomic position of a crystal in a three-dimensional (3D) space [7].…”

Section: Introductionmentioning

confidence: 99%

SPRSF: Sparse Phase Retrieval via Smoothing Function

Pinilla,

Bacca,

Arguello

2018

Preprint

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Phase retrieval (PR) is an ill-conditioned inverse problem which can be found in various science and engineering applications. Assuming sparse priority over the signal of interest, recent algorithms have been developed to solve the phase retrieval problem. Some examples include SparseAltMinPhase (SAMP), Sparse Wirtinger flow (SWF) and Sparse Truncated Amplitude flow (SPARTA). However, the optimization cost functions of the mentioned algorithms are nonconvex and non-smooth. In order to fix the non-smoothness of the cost function, the SPARTA method uses truncation thresholds to calculate a truncated step update direction. In practice, the truncation procedure requires calculating more parameters to obtain a desired performance in the phase recovery. Therefore, this paper proposes an algorithm called SPRSF (Sparse Phase retrieval via Smoothing Function) to solve the sparse PR problem by introducing a smoothing function. SPRSF is an iterative algorithm where the update step is obtained by a hard thresholding over a gradient descent direction. Theoretical analyses show that the smoothing function uniformly approximates the non-convex and non-smooth sparse PR optimization problem. Moreover, SPRSF does not require the truncation procedure used in SPARTA. Numerical tests demonstrate that SPRSF performs better than state-of-the-art methods, especially when there is no knowledge about the sparsity k. In particular, SPRSF attains a higher mean recovery rate in comparison with SPARTA, SAMP and SWF methods, when the sparsity varies for the real and complex cases. Further, in terms of the sampling complexity, the SPRSF method outperforms its competitive alternatives.

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Coded diffraction system in X-ray crystallography using a boolean phase coded aperture approximation

Cited by 15 publications

References 15 publications

Deep Coded Aperture Design: An End-to-End Approach for Computational Imaging Tasks

Deep Coded Aperture Design: An End-to-End Approach for Computational Imaging Tasks

A Smoothing Stochastic Phase Retrieval Algorithm for Solving Random Quadratic Systems

SPRSF: Sparse Phase Retrieval via Smoothing Function

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