Problem Of Optical Tomography Research Articles

Nonlinear self-calibrated spectrometer with single GeSe-InSe heterojunction device.

Computational spectrometry is an emerging field that uses photodetection in conjunction with numerical algorithms for spectroscopic measurements. Compact single photodetectors made from layered materials are particularly attractive since they eliminate the need for bulky mechanical and optical components used in traditional spectrometers and can easily be engineered as heterostructures to optimize device performance. However, such photodetectors are typically nonlinear devices, which adds complexity to extracting optical spectra from their response. Here, we train an artificial neural network to recover the full nonlinear spectral photoresponse of a single GeSe-InSe p-n heterojunction device. The device has a spectral range of 400 to 1100 nm, a small footprint of ~25 × 25 square micrometers, and a mean reconstruction error of 2 × 10-4 for the power spectrum at 0.35 nanometers. Using our device, we demonstrate a solution to metamerism, an apparent matching of colors with different power spectral distributions, which is a fundamental problem in optical imaging.

On the imaging depth limit of photoacoustic tomography in the visible and first near-infrared windows.

It is well known that photoacoustic tomography (PAT) can circumvent the photon scattering problem in optical imaging and achieve high-contrast and high-resolution imaging at centimeter depths. However, after two decades of development, the long-standing question of the imaging depth limit of PAT in biological tissues remains unclear. Here we propose a numerical framework for evaluating the imaging depth limit of PAT in the visible and the first near-infrared windows. The established framework simulates the physical process of PAT and consists of seven modules, including tissue modelling, photon transportation, photon to ultrasound conversion, sound field propagation, signal reception, image reconstruction, and imaging depth evaluation. The framework can simulate the imaging depth limits in general tissues, such as the human breast, the human abdomen-liver tissues, and the rodent whole body and provide accurate evaluation results. The study elucidates the fundamental imaging depth limit of PAT in biological tissues and can provide useful guidance for practical experiments.

General relations for optical design parameters under diffraction limited paraxial imaging

We searched for fundamental relationships among general optical system parameters assuming diffraction limited imaging in paraxial space. We demonstrated that the total twelve optical system parameters describing the optical imaging problem are unambiguously determined with a set of four of them. This holds for a diffraction condition, where the image permitted blur is of the same size for both the spot due to defocus and the diffraction spot. Depending on the combinations of the four input parameters there can be found up to 314 different optical system design approaches to fully describe the diffraction limited imaging problem. We demonstrated eight examples of optical system design approaches using different combinations of input parameters. It can be helpful for optical designers to decide if diffraction limited imaging is feasible for the desired combination of optical imaging system parameters. With the reduction of the optical system to a thin lens approximation, the number of the optical system parameters describing the optical imaging problem decreases to eight and its unambiguous determination is possible with a set of only three of these parameters. It provides, up to 54 optical system design approaches based on different combinations of input parameters.

Motion detection in diffraction tomography by common circle methods

The method of common lines is a well-established reconstruction technique in cryogenic electron microscopy (cryo-EM), which can be used to extract the relative orientations of an object given tomographic projection images from different directions. In this paper, we deal with an analogous problem in optical diffraction tomography. Based on the Fourier diffraction theorem, we show that rigid motions of the object, i.e., rotations and translations, can be determined by detecting common circles in the Fourier-transformed data. We introduce two methods to identify common circles. The first one is motivated by the common line approach for projection images and detects the relative orientation by parameterizing the common circles in the two images. The second one assumes a smooth motion over time and calculates the angular velocity of the rotational motion via an infinitesimal version of the common circle method. Interestingly, using the stereographic projection, both methods can be reformulated as common line methods, but these lines are, in contrast to those used in cryo-EM, not confined to pass through the origin and allow for a full reconstruction of the relative orientations. Numerical proof-of-the-concept examples demonstrate the performance of our reconstruction methods.

Learn an Index Operator by CNN for Solving Diffusive Optical Tomography: A Deep Direct Sampling Method

In this work, we investigate the diffusive optical tomography (DOT) problem in the case that limited boundary measurements are available. Motivated by the direct sampling method (DSM) proposed in Chow et al. (SIAM J Sci Comput 37(4):A1658–A1684, 2015), we develop a deep direct sampling method (DDSM) to recover the inhomogeneous inclusions buried in a homogeneous background. In this method, we design a convolutional neural network to approximate the index functional that mimics the underling mathematical structure. The benefits of the proposed DDSM include fast and easy implementation, capability of incorporating multiple measurements to attain high-quality reconstruction, and advanced robustness against the noise. Numerical experiments show that the reconstruction accuracy is improved without degrading the efficiency, demonstrating its potential for solving the real-world DOT problems.

On the inverse problem in optical coherence tomography

We examine the inverse problem of retrieving sample refractive index information in the context of optical coherence tomography. Using two separate approaches, we discuss the limitations of the inverse problem which lead to it being ill-posed, primarily as a consequence of the limited viewing angles available in the reflection geometry. This is first considered from the theoretical point of view of diffraction tomography under a weak scattering approximation. We then investigate the full non-linear inverse problem using a variational approach. This presents another illustration of the non-uniqueness of the solution, and shows that even the non-linear (strongly scattering) scenario suffers a similar fate as the linear problem, with the observable spatial Fourier components of the sample occupying a limited support. Through examples we demonstrate how the solutions to the inverse problem compare when using the variational and diffraction-tomography approaches.

Level set‐based shape optimization approach for the inverse optical tomography problem

Level set‐based shape optimization approach for the inverse optical tomography problem

Dielectric Metalens for Superoscillatory Focusing Based on High-Order Angular Bessel Function.

The phenomenon of optical superoscillation provides an unprecedented way to solve the problem of optical far-field label-free super-resolution imaging. Numerous optical devices that enable superoscillatory focusing were developed based on scalar and vector diffraction theories in the past several years. However, these reported devices are designed according to the half-wave zone method in spatial coordinates. In this paper, we propose a dielectric metalens for superoscillatory focusing based on the diffraction of angular Bessel functional phase modulated vector field, under the inspiration of the tightly autofocusing property of a radially polarized high-order Bessel beam. Based on this kind of metalens with a numerical aperture (NA) of 0.9, the linearly polarized light is converted into a radially polarized one and then focus into a superoscillating focal spot with the size of 0.32λ/NA. This angular spectrum modulation theory involved in this paper provides a different way of designing superoscillatory devices.

Parallel inverse-problem solver for time-domain optical tomography with perfect parallel scaling

This paper presents an efficient parallel radiative transfer-based inverse-problem solver for time-domain optical tomography. The radiative transfer equation provides a physically accurate model for the transport of photons in biological tissue, but the high computational cost associated with its solution has hindered its use in time-domain optical-tomography and other areas. In this paper this problem is tackled by means of a number of computational and modeling innovations, including (1) A spatial parallel-decomposition strategy with perfect parallel scaling for the forward and inverse problems of optical tomography on parallel computer systems; and, (2) A Multiple Staggered Source method (MSS) that solves the inverse transport problem at a computational cost that is independent of the number of sources employed, and which significantly accelerates the reconstruction of the optical parameters: a six-fold MSS acceleration factor is demonstrated in this paper. Finally, this contribution presents (3) An intuitive derivation of the adjoint-based formulation for evaluation of functional gradients, including the highly-relevant general Fresnel boundary conditions—thus, in particular, generalizing results previously available for vacuum boundary conditions. Solutions of large and realistic 2D inverse problems are presented in this paper, which were produced on a 256-core computer system. The combined parallel/MSS acceleration approach reduced the required computing times by several orders of magnitude, from months to a few hours.

Blind inverse problems with isolated spikes

Abstract Assume that an unknown integral operator living in some known subspace is observed indirectly, by evaluating its action on a discrete measure containing a few isolated Dirac masses at an unknown location. Is this information enough to recover the impulse response location and the operator with a sub-pixel accuracy? We study this question and bring to light key geometrical quantities for exact and stable recovery. We also propose an in-depth study of the presence of additive white Gaussian noise. We illustrate the well-foundedness of this theory on the challenging optical imaging problem of blind deconvolution and blind deblurring with non-stationary operators.

Bridging and Improving Theoretical and Computational Electrical Impedance Tomography via Data Completion

In computational PDE-based inverse problems, a finite amount of data is collected to infer unknown parameters in the PDE. In order to obtain accurate inferences, the collected data must be informative about the unknown parameters. How to decide which data is most informative and how to efficiently sample it is the notoriously challenging task of optimal experimental design (OED). In this context, the best, and often infeasible, scenario is when the full input-to-output (ItO) map, i.e., an infinite amount of data, is available: This is the typical setting in many theoretical inverse problems, which is used to guarantee the unique parameter reconstruction. These two different settings have created a gap between computational and theoretical inverse problems, where finite and infinite amounts of data are used, respectively. In this article we aim to bridge this gap while circumventing the OED task. This is achieved by exploiting the structures of the ItO data from the underlying inverse problem, using the electrical impedance tomography (EIT) problem as an example. To accomplish our goal, we leverage the rank structure of the EIT model and formulate the ItO matrix\textemdash the discretized ItO map\textemdash as an $\mathcal{H}$-matrix whose off-diagonal blocks are low rank. This suggests that, when equipped with the matrix completion technique, one can recover the full ItO matrix, with high probability, from a subset of its entries sampled following the rank structure: The data in the diagonal blocks is informative and should be fully sampled, while data in the off-diagonal blocks can be subsampled. This recovered ItO matrix is then utilized to present the full ItO map up to a discretization error, paving the way to connect with the problem in the theoretical setting where the unique reconstruction of parameters is guaranteed. This strategy achieves two goals: (I) it bridges the gap between the finite- and infinite-dimensional settings for numerical and theoretical inverse problems and (II) it improves the quality of computational inverse solutions. We detail the theory for the EIT model and provide numerical verification to both EIT and optical tomography problems.

Fourier reconstruction for diffraction tomography of an object rotated into arbitrary orientations

In this paper, we study the mathematical imaging problem of optical diffraction tomography (ODT) for the scenario of a microscopic rigid particle rotating in a trap created, for instance, by acoustic or optical forces. Under the influence of the inhomogeneous forces the particle carries out a time-dependent smooth, but irregular motion described by a set of affine transformations. The rotation of the particle enables one to record optical images from a wide range of angles, which largely eliminates the ‘missing cone problem’ in optics. This advantage, however, comes at the price that the rotation axis in this scenario is not fixed, but continuously undergoes some variations, and that the rotation angles are not equally spaced, which is in contrast to standard tomographic reconstruction assumptions. In the present work, we assume that the time-dependent motion parameters are known, and that the particle’s scattering potential is compatible with making the first order Born or Rytov approximation. We prove a Fourier diffraction theorem and derive novel backpropagation formulae for the reconstruction of the scattering potential, which depends on the refractive index distribution inside the object, taking its complicated motion into account. This provides the basis for solving the ODT problem with an efficient non-uniform discrete Fourier transform.

De-noising imaging through diffusers with autocorrelation.

Recovering targets through diffusers is an important topic as well as a general problem in optical imaging. The difficulty of recovering is increased due to the noise interference caused by an imperfect imaging environment. Existing approaches generally require a high-signal-to-noise-ratio (SNR) speckle pattern to recover the target, but still have limitations in de-noising or generalizability. Here, featuring information of high-SNR autocorrelation as a physical constraint, we propose a two-stage (de-noising and reconstructing) method to improve robustness based on data driving. Specifically, a two-stage convolutional neural network (CNN) called autocorrelation reconstruction (ACR) CNN is designed to de-noise and reconstruct targets from low-SNR speckle patterns. We experimentally demonstrate the robustness through various diffusers with different levels of noise, from simulative Gaussian noise to the detector and photon noise captured by the actual optical system. The de-noising stage improves the peak SNR from 20 to 38 dB in the system data, and the reconstructing stage, compared with the unconstrained method, successfully recovers targets hidden in unknown diffusers with the detector and photon noise. With the help of the physical constraint to optimize the learning process, our two-stage method is realized to improve generalizability and has potential in various fields such as imaging in low illumination.

A model reduction approach for inverse problems with operator valued data

We study the efficient numerical solution of linear inverse problems with operator valued data which arise, e.g., in seismic exploration, inverse scattering, or tomographic imaging. The high-dimensionality of the data space implies extremely high computational cost already for the evaluation of the forward operator which makes a numerical solution of the inverse problem, e.g., by iterative regularization methods, practically infeasible. To overcome this obstacle, we take advantage of the underlying tensor product structure of the problem and propose a strategy for constructing low-dimensional certified reduced order models of quasi-optimal rank for the forward operator which can be computed much more efficiently than the truncated singular value decomposition. A complete analysis of the proposed model reduction approach is given in a functional analytic setting and the efficient numerical construction of the reduced order models as well as of their application for the numerical solution of the inverse problem is discussed. In summary, the setup of a low-rank approximation can be achieved in an offline stage at essentially the same cost as a single evaluation of the forward operator, while the actual solution of the inverse problem in the online phase can be done with extremely high efficiency. The theoretical results are illustrated by application to a typical model problem in fluorescence optical tomography.

Refractive three-dimensional reconstruction for underwater stereo digital image correlation.

Measuring the three-dimensional (3D) deformation of submerged objects through different media with the stereo digital image correlation (stereo-DIC) method involves the refractive optical imaging problem where the non-linear transmission of light is induced by a change of medium density. The problem invalidates the underlying single viewpoint assumption of the perspective model in regular stereo-DIC, thereby resulting in erroneous measurements of 3D shape and deformation. In this work, we propose a refractive stereo-DIC method that overcomes the problem by considering light refraction in 3D reconstruction. We formulate a full refractive reconstruction geometry description based on Snell's law of flat refraction and the regular triangulation. This allows the true shape to be effectively reconstructed by tracing and establishing the refracted ray-paths based on the regular 3D reconstruction, without reformulating the camera model and image formation. The refractive stereo-DIC is finally established by integrating the refractive 3D reconstruction into the regular DIC framework for measuring accurate 3D shape and deformation of submerged objects. We experiment the proposed approach with underwater 3D shape and deformation measurements. Both results prove its feasibility and correctness, further heralding our approach as a flexible solution that could readily extend the stereo-DIC to fluid-immersed 3D deformation characterization.

PAMSGAN: Pyramid Attention Mechanism-Oriented Symmetry Generative Adversarial Network for Motion Image Deblurring

Motion blur is a common problem in optical imaging, which is caused by the relative displacement between the subject and the camera in the exposure process of the camera. This can result in motion blur of the acquired image, reduce the image resolution and affect the imaging quality. Motion blur image restoration technology uses the existing motion blur image to restore the clear image through the modeling of imaging physical process and mathematical solution without re-photographing the target scene. It has an important application value in the civil and military fields. Solving the problem of motion blur caused by camera jitter and object motion during camera imaging is a very challenging problem. When the popular generative adversarial network model is directly applied to the image blur blind removal task, serious pattern collapse phenomenon will occur. In this paper, we propose a novel motion image deblurring model based on pyramid attention mechanism-oriented symmetry generative adversarial network. This new method does not need to predict the fuzzy kernel of the blurred images, and can directly realize the blind removal of image motion blur. Based on the original CycleGan, the network structure and loss function of the symmetry generative adversarial network are improved. The accuracy of blind removal of motion images is improved, and the stability of the network is greatly enhanced in the case of limited samples. The generative network adopts the encoding and decoding structure, and introduces the feature pyramid attention mechanism. The combination of multi-scale pyramid features and attention mechanism can capture more rich advanced features to improve the model performance. In the experiment, the RMSProp algorithm is used to optimize the network training. Finally, a clear image is obtained through network adversarial training between generative and discriminant network. Experimental results on the related image blur benchmark datasets show that the restoration quality of the proposed method is higher in terms of subjective and objective evaluation. Meanwhile, the restoration results can achieve better results in subsequent object detection tasks.

Uniqueness, Lipschitz Stability, and Reconstruction for the Inverse Optical Tomography Problem

In this paper, we consider the inverse problem of recovering a diffusion $\sigma$ and absorption coefficients $q$ in a steady-state optical tomography problem from the Neumann-to-Dirichlet map. We ...

Efficient inversion strategies for estimating optical properties with Monte Carlo radiative transport models.

.Significance: Indirect imaging problems in biomedical optics generally require repeated evaluation of forward models of radiative transport, for which Monte Carlo is accurate yet computationally costly. We develop an approach to reduce this bottleneck, which has significant implications for quantitative tomographic imaging in a variety of medical and industrial applications.Aim: Our aim is to enable computationally efficient image reconstruction in (hybrid) diffuse optical modalities using stochastic forward models.Approach: Using Monte Carlo, we compute a fully stochastic gradient of an objective function for a given imaging problem. Leveraging techniques from the machine learning community, we then adaptively control the accuracy of this gradient throughout the iterative inversion scheme to substantially reduce computational resources at each step.Results: For example problems of quantitative photoacoustic tomography and ultrasound-modulated optical tomography, we demonstrate that solutions are attainable using a total computational expense that is comparable to (or less than) that which is required for a single high-accuracy forward run of the same Monte Carlo model.Conclusions: This approach demonstrates significant computational savings when approaching the full nonlinear inverse problem of optical property estimation using stochastic methods.

Lipschitz stability at the boundary for time-harmonic diffuse optical tomography

ABSTRACT We study the inverse problem in Optical Tomography of determining the optical properties of a medium , with , under the so-called diffusion approximation. We consider the time-harmonic case where Ω is probed with an input field that is modulated with a fixed harmonic frequency , where c is the speed of light and k is the wave number. We prove a result of Lipschitz stability of the absorption coefficient at the boundary in terms of the measurements in the case when the scattering coefficient is assumed to be known and k belongs to certain intervals depending on some a-priori bounds on , .

Does deep learning always outperform simple linear regression in optical imaging?

Deep learning has been extensively applied in many optical imaging problems in recent years. Despite the success, the limitations and drawbacks of deep learning in optical imaging have been seldom investigated. In this work, we show that conventional linear-regression-based methods can outperform the previously proposed deep learning approaches for two black-box optical imaging problems in some extent. Deep learning demonstrates its weakness especially when the number of training samples is small. The advantages and disadvantages of linear-regression-based methods and deep learning are analyzed and compared. Since many optical systems are essentially linear, a deep learning network containing many nonlinearity functions sometimes may not be the most suitable option.