SEAGLE: Sparsity-Driven Image Reconstruction Under Multiple Scattering

Liu, Hsiou-Yuan; Liu, Dehong; Mansour, Hassan; Boufounos, Petros T.; Waller, Laura; Kamilov, Ulugbek S.

doi:10.1109/tci.2017.2764461

Cited by 69 publications

(81 citation statements)

References 86 publications

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“…To demonstrate its versatility, we use DP-DT to improve the quality of 3D sample reconstruction under the assumptions of both the first Born [8] and MS approximations [10,17,18]. While the rest of this section assumes that we are reconstructing with phaseless measurements, we note that the DIP pipeline can easily be applied with different assumed forward models (e.g., [46][47][48]), and can be also applied to phase-sensitive measurements from traditional DT setups, which we include examples of in Appendix C. Fig. 3 shows a high-level summary of the forward image formation process and the inverse problem formulation, with mathematical details presented in Appendix B.…”

Section: Deep Prior Diffraction Tomography (Dp-dt)mentioning

confidence: 99%

Diffraction tomography with a deep image prior

Zhou¹,

Horstmeyer²

2020

Opt. Express

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We present a tomographic imaging technique, termed Deep Prior Diffraction Tomography (DP-DT), to reconstruct the 3D refractive index (RI) of thick biological samples at high resolution from a sequence of low-resolution images collected under angularly varying illumination. DP-DT processes the multi-angle data using a phase retrieval algorithm that is extended by a deep image prior (DIP), which reparameterizes the 3D sample reconstruction with an untrained, deep generative 3D convolutional neural network (CNN). We show that DP-DT effectively addresses the missing cone problem, which otherwise degrades the resolution and quality of standard 3D reconstruction algorithms. As DP-DT does not require pre-captured data or pre-training, it is not biased towards any particular dataset. Hence, it is a general technique that can be applied to a wide variety of 3D samples, including scenarios in which large datasets for supervised training would be infeasible or expensive. We applied DP-DT to obtain 3D RI maps of bead phantoms and complex biological specimens, both in simulation and experiment, and show that DP-DT produces higher-quality results than standard regularization techniques. We further demonstrate the generality of DP-DT, using two different scattering models, the first Born and multi-slice models. Our results point to the potential benefits of DP-DT for other 3D imaging modalities, including X-ray computed tomography, magnetic resonance imaging, and electron microscopy.

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Section: Deep Prior Diffraction Tomography (Dp-dt)mentioning

confidence: 99%

Diffraction tomography with a deep image prior

Zhou¹,

Horstmeyer²

2020

Opt. Express

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“…To do so, we first discretize Ω into N = n 3 voxels 1 . Then, the computation of the scattered field y sc ∈ C M at the camera plane Γ follows a two-step process [17,18],…”

Section: Discrete Formulationmentioning

confidence: 99%

“…Following [17][18][19], we deploy an accelerated forward-backward splitting (FBS) algorithm [41,42] to solve the optimization problem (17). The iterates are summarized in Algorithm 1, with some further details below.…”

Section: Optimizationmentioning

confidence: 99%

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Three-Dimensional Optical Diffraction Tomography With Lippmann-Schwinger Model

Pham

Soubies

Ayoub

et al. 2020

IEEE Trans. Comput. Imaging

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A broad class of imaging modalities involve the resolution of an inverse-scattering problem. Among them, three-dimensional optical diffraction tomography (ODT) comes with its own challenges. These include a limited range of views, a large size of the sample with respect to the illumination wavelength, and optical aberrations that are inherent to the system itself. In this work, we present an accurate and efficient implementation of the forward model. It relies on the exact (nonlinear) Lippmann-Schwinger equation. We address several crucial issues such as the discretization of the Green function, the computation of the far field, and the estimation of the incident field. We then deploy this model in a regularized variational-reconstruction framework and show on both simulated and real data that it leads to substantially better reconstructions than the approximate models that are traditionally used in ODT. IntroductionOptical diffraction tomography (ODT) is a noninvasive quantitative imaging modality [1,2]. This label-free technique allows one to determine a three-dimensional map of the refractive index (RI) of samples, which is of particular interest for applications that range from biology [3] to nanotechnologies [4]. The acquisition setup sequentially illuminates the sample from different angles. For each illumination, the outgoing complex wave field (i.e., the scattered field) is recorded by a digital-holography microscope [5,6]. Then, from this set of measurements, the RI of the sample can be reconstructed by solving an inverse-scattering problem. However, its resolution is very challenging due to the nonlinear nature of the interaction between the light and the sample. Related WorksTo simplify the reconstruction problem, pioneering works focused on linearized models. These include Born [1] and Rytov [7] approximations, which are valid for weakly scattering samples [8]. Although originally used to deploy direct inversion methods, these linearized models have been later combined with iterative regularization techniques to improve their robustness to noise and to alleviate the missing-cone problem [9,10].Nonlinear models that adhere more closely to the physic of the acquisition are needed to recover samples with higher variations of their refractive index. For instance, beam-propagation methods (BPM) [11][12][13][14] rely on a slice-by-slice propagation model that accounts for multiple scatterings within the direction of propagation (no reflection). Other nonlinear models include the contrast source-inversion method [15] or the recursive Born approximation [16]. Although more accurate, all these models come at the price of a large computational cost.The theory of scalar diffraction recognizes the Lippmann-Schwinger (LS) model to be the most faithful. It accounts for multiple scatterings, both in transmission and reflection. Iterative forward models that solve the LS equation have

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“…Reconstruction algorithms that consider the nonlinear process have recently been proposed [19][20][21]. We focus on the beam propagation method (BPM), which can be used as the propagation model combined with sparsity-based regularization in the iterative reconstruction scheme [20].…”

Section: Introductionmentioning

confidence: 99%

Learning Tomography Assessed Using Mie Theory

et al. 2018

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In optical diffraction tomography, the multiply scattered field is a nonlinear function of the refractive index (RI) of the object. The Rytov method relies on a single-scattering propagation model and is commonly used to reconstruct images. Recently, a reconstruction model was introduced based on the beam propagation method that takes multiple scattering into account. We refer to this method as learning tomography (LT). We carry out simulations and experiments in order to assess the performance of LT over the iterative single-scattering propagation method. Each algorithm is rigorously assessed for spherical and cylinderical objects, with synthetic data generated using Mie theory. By varying the RI contrast and the size of the objects, we show that the LT reconstruction is more accurate and robust than the reconstruction based on the single-scattering propagation model. In addition, we show that LT is able to correct distortions that are evident in the Rytov-approximation-based reconstructions due to limitations in phase unwrapping. More importantly, the ability of LT to handle multiple scattering is demonstrated by simulations of multiple cylinders using Mie theory and is confirmed by experiment.

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SEAGLE: Sparsity-Driven Image Reconstruction Under Multiple Scattering

Cited by 69 publications

References 86 publications

Diffraction tomography with a deep image prior

Diffraction tomography with a deep image prior

Three-Dimensional Optical Diffraction Tomography With Lippmann-Schwinger Model

Learning Tomography Assessed Using Mie Theory

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