arXiv subjects

Yukun Guo

Publications and source records attributed to Yukun Guo.

At least 37 records · Page 2Linked to original sources

arXiv2023

Multipolar Acoustic Source Reconstruction from Sparse Far-Field Data using ALOHA

The reconstruction of multipolar acoustic or electromagnetic sources from their far-field signature plays a crucial role in numerous applications. Most of the existing techniques require dense multi-frequency data at the Nyquist sampling rate. The availability of a sub-sampled grid contributes to the null space of the inverse source-to-data operator, which causes significant imaging artifacts. For this purpose, additional knowledge about the source or regularization is required. In this letter, we propose a novel two-stage strategy for multipolar source reconstruction from sub-sampled sparse data that takes advantage of the sparsity of the sources in the physical domain. The data at the Nyquist sampling rate is recovered from sub-sampled data and then a conventional inversion algorithm is used to reconstruct sources. The data recovery problem is linked to a spectrum recovery problem for the signal with the \textit{finite rate of innovations} (FIR) that is solved using an annihilating filter-based structured Hankel matrix completion approach (ALOHA). For an accurate reconstruction, a Fourier inversion algorithm is used. The suitability of the approach is supported by experiments.

cs.IT↗

arXiv2023

A novel Newton method for inverse elastic scattering problems

This work is concerned with an inverse elastic scattering problem of identifying the unknown rigid obstacle embedded in an open space filled with a homogeneous and isotropic elastic medium. A Newton-type iteration method relying on the boundary condition is designed to identify the boundary curve of the obstacle. Based on the Helmholtz decomposition and the Fourier-Bessel expansion, we explicitly derive the approximate scattered field and its derivative on each iterative curve. Rigorous mathematical justifications for the proposed method are provided. Numerical examples are presented to verify the effectiveness of the proposed method.

math.NA↗

arXiv2023

Perfused and Nonperfused Microaneurysms Identified and Characterized by Structural and Angiographic OCT

Purpose: Microaneurysms (MAs) have distinct, oval-shaped, hyperreflective walls on structural OCT, and inconsistent flow signal in the lumen with OCT angiography (OCTA). Their relationship to regional macular edema in diabetic retinopathy (DR) has not been quantitatively explored. Participants: A total of 99 participants, including 23 with mild, NPDR, 25 with moderate NPDR, 34 with severe NPDR, and 17 with proliferative DR. Methods: We obtained 3 x 3-mm scans with a commercial device (Solix, Visionix/Optovue) in 99 patients with DR. Trained graders manually identified MAs and their location relative to the anatomic layers from cross-sectional OCT. Microaneurysms were first classified as perfused if flow signal was present in the OCTA channel. Then, perfused MAs were further classified into fully and partially perfused MAs based on the flow characteristics in en face OCTA. The presence of retinal fluid based on OCT near MAs was compared between perfused and nonperfused types. We also compared OCT-based MA detection to fundus photography (FP)- and fluorescein angiography (FA)-based detection. Results: We identified 308 MAs (166 fully perfused, 88 partially perfused, 54 nonperfused) in 42 eyes using OCT and OCTA. Nearly half of the MAs identified in this study straddle the inner nuclear layer and outer plexiform layer. Compared with partially perfused and nonperfused MAs, fully perfused MAs were more likely to be associated with local retinal fluid. The associated fluid volumes were larger with fully perfused MAs compared with other types. OCT/OCTA detected all MAs found on FP. Although not all MAs seen with FA were identified with OCT, some MAs seen with OCT were not visible with FA or FP. Conclusions: OCT-identified MAs with colocalized flow on OCTA are more likely to be associated with DME than those without flow.

q-bio.QM↗

arXiv2023

Mathematical and numerical study of an inverse source problem for the biharmonic wave equation

In this paper, we study the inverse source problem for the biharmonic wave equation. Mathematically, we characterize the radiating sources and non-radiating sources at a fixed wavenumber. We show that a general source can be decomposed into a radiating source and a non-radiating source. The radiating source can be uniquely determined by Dirichlet boundary measurements at a fixed wavenumber. Moreover, we derive a Lipschitz stability estimate for determining the radiating source. On the other hand, the non-radiating source does not produce any scattered fields outside the support of the source function. Numerically, we propose a novel source reconstruction method based on Fourier series expansion by multi-wavenumber boundary measurements. Numerical experiments are presented to verify the accuracy and efficiency of the proposed method.

math.NA↗

arXiv2023

Interpretable Diabetic Retinopathy Diagnosis based on Biomarker Activation Map

Deep learning classifiers provide the most accurate means of automatically diagnosing diabetic retinopathy (DR) based on optical coherence tomography (OCT) and its angiography (OCTA). The power of these models is attributable in part to the inclusion of hidden layers that provide the complexity required to achieve a desired task. However, hidden layers also render algorithm outputs difficult to interpret. Here we introduce a novel biomarker activation map (BAM) framework based on generative adversarial learning that allows clinicians to verify and understand classifiers decision-making. A data set including 456 macular scans were graded as non-referable or referable DR based on current clinical standards. A DR classifier that was used to evaluate our BAM was first trained based on this data set. The BAM generation framework was designed by combing two U-shaped generators to provide meaningful interpretability to this classifier. The main generator was trained to take referable scans as input and produce an output that would be classified by the classifier as non-referable. The BAM is then constructed as the difference image between the output and input of the main generator. To ensure that the BAM only highlights classifier-utilized biomarkers an assistant generator was trained to do the opposite, producing scans that would be classified as referable by the classifier from non-referable scans. The generated BAMs highlighted known pathologic features including nonperfusion area and retinal fluid. A fully interpretable classifier based on these highlights could help clinicians better utilize and verify automated DR diagnosis.

eess.IV↗

arXiv2023

Jointly determining the point sources and obstacle from Cauchy data

A numerical method is developed for recovering both the source locations and the obstacle from the scattered Cauchy data of the time-harmonic acoustic field. First of all, the incident and scattered components are decomposed from the coupled Cauchy data by the representation of the single-layer potentials and the solution to the resulting linear integral system. As a consequence of this decomposition, the original problem of joint inversion is reformulated into two decoupled subproblems: an inverse source problem and an inverse obstacle scattering problem. Then, two sampling-type schemes are proposed to recover the shape of the obstacle and the source locations, respectively. The sampling methods rely on the specific indicator functions defined on target-oriented probing domains of circular shape. The error estimates of the decoupling procedure are established and the asymptotic behaviors of the indicator functions are analyzed. Extensive numerical experiments are also conducted to verify the performance of the sampling schemes.

math.NA↗

arXiv2023

Recovering source location, polarization, and shape of obstacle from elastic scattering data

We consider an inverse elastic scattering problem of simultaneously reconstructing a rigid obstacle and the excitation sources using near-field measurements. A two-phase numerical method is proposed to achieve the co-inversion of multiple targets. In the first phase, we develop several indicator functionals to determine the source locations and the polarizations from the total field data, and then we manage to obtain the approximate scattered field. In this phase, only the inner products of the total field with the fundamental solutions are involved in the computation, and thus it is direct and computationally efficient. In the second phase, we propose an iteration method of Newton's type to reconstruct the shape of the obstacle from the approximate scattered field. Using the layer potential representations on an auxiliary curve inside the obstacle, the scattered field together with its derivative on each iteration surface can be easily derived. Theoretically, we establish the uniqueness of the co-inversion problem and analyze the indicating behavior of the sampling-type scheme. An explicit derivative is provided for the Newton-type method. Numerical results are presented to corroborate the effectiveness and efficiency of the proposed method.

math.NA↗

arXiv2022

Imaging an acoustic obstacle and its excitation sources from phaseless near-field data

This paper is concerned with reconstructing an acoustic obstacle and its excitation sources from the phaseless near-field measurements. By supplementing some artificial sources to the inverse scattering system, this co-inversion problem can be decoupled into two inverse problems: an inverse obstacle scattering problem and an inverse source problem, and the corresponding uniqueness can be established. This novel decoupling technique requires some extra data but brings in several salient benefits. First, our method is fast and easy to implement. Second, the boundary condition of the obstacle is not needed. Finally, this approximate decoupling method can be applied to other co-inversion problems, such as determining the medium and its excitation sources. Several numerical examples are presented to demonstrate the feasibility and effectiveness of the proposed method.

math.NA↗

arXiv2022

Bichromatic state-dependent disordered potential for Anderson localization of ultracold atoms

The ability to load ultracold atoms at a well-defined energy in a disordered potential is a crucial tool to study quantum transport, and in particular Anderson localization. In this paper, we present a new method for achieving that goal by rf transfer of atoms of an atomic Bose-Einstein condensate from a disorder insensitive state to a disorder sensitive state. It is based on a bichromatic laser speckle pattern, produced by two lasers whose frequencies are chosen so that their light-shifts cancel each other in the first state and add-up in the second state. Moreover, the spontaneous scattering rate in the disorder-sensitive state is low enough to allow for long observation times of quantum transport in that state. We theoretically and experimentally study the characteristics of the resulting potential.

cond-mat.quant-gas↗

arXiv2022

Co-inversion of a scattering cavity and its internal sources: uniqueness, decoupling and imaging

This paper concerns the simultaneous reconstruction of a sound-soft cavity and its excitation sources from the total-field data. Using the single-layer potential representations on two measurement curves, this co-inversion problem can be decoupled into two inverse problems: an inverse cavity scattering problem and an inverse source problem. This novel decoupling technique is fast and easy to implement since it is based on a linear system of integral equations. Then the uncoupled subproblems are respectively solved by the modified optimization and sampling method. We also establish the uniqueness of this co-inversion problem and analyze the stability of our method. Several numerical examples are presented to demonstrate the feasibility and effectiveness of the proposed method.

math.NA↗

arXiv2022

A direct imaging method for the exterior and interior inverse scattering problems

This paper is concerned with the inverse acoustic scattering problems by an obstacle or a cavity with a sound-soft or a sound-hard boundary. A direct imaging method relying on the boundary conditions is proposed for reconstructing the shape of the obstacle or cavity. First, the scattered fields are approximated by the Fourier-Bessel functions with the measurements on a closed curve. Then, the indicator functions are established by the superpositions of the total fields or their derivatives to the incident point sources. We prove that the indicator functions vanish only on the boundary of the obstacle or cavity. Numerical examples are also included to demonstrate the effectiveness of the method.

math.NA↗

arXiv2021

Simultaneous recovery of an obstacle and its excitation sources from near-field scattering data

This paper is concerned with the inverse problem of determining an obstacle and the corresponding incident point sources in the Helmholtz equation from near-field scattering data. An optimization method is proposed to simultaneously recover both the obstacle and source locations. Moreover, a two-step sampling scheme with novel indicator functions is proposed to produce a good initial guess for solving the optimization problem. Theoretically, we analyze the convergence properties of the optimization method and the indicating behaviors of the indicator functions. Several numerical examples are presented to show the effectiveness of the proposed method.

math.AP↗

arXiv2021

Computation of transmission eigenvalues by the regularized Schur complement for the boundary integral operators

This paper is devoted to the computation of transmission eigenvalues in the inverse acoustic scattering theory. This problem is first reformulated as a two by two boundary system of boundary integral equations. Next, utilizing the Schur complement technique, we develop a Schur complement operator with regularization to obtain a reduced system of boundary integral equations. The Nyström discretization is then used to obtain an eigenvalue problem for a matrix. We employ the recursive integral method for the numerical computation of the matrix eigenvalue. Numerical results show that the proposed method is efficient and reduces computational costs.

math.NA↗

arXiv2021

Direct imaging for the moment tensor point sources of elastic waves

We investigate an inverse source problem of the time-harmonic elastic wave equation. Some novel sampling-type numerical schemes are proposed to identify the moment tensor point sources in the Lamé system from near-field measurements. Rigorous theoretical justifications are provided to show that the locations and moment tensors of the elastic sources can be uniquely determined from the multi-frequency displacement data. Several numerical examples are also presented to illustrate the validity and robustness of the proposed method.

math.NA↗

arXiv2021

A deterministic-statistical approach to reconstruct moving sources using sparse partial data

We consider the reconstruction of moving sources using partial measured data. A two-step deterministic-statistical approach is proposed. In the first step, an approximate direct sampling method is developed to obtain the locations of the sources at different times. Such information is coded in the priors, which is critical for the success of the Bayesian method in the second step. The well-posedness of the posterior measure is analyzed in the sense of the Hellinger distance. Both steps are based on the same physical model and use the same set of measured data. The combined approach inherits the merits of the deterministic method and Bayesian inversion as demonstrated by the numerical examples.

math.NA↗

arXiv2020

Reconstruction of high-resolution 6x6-mm OCT angiograms using deep learning

Typical optical coherence tomographic angiography (OCTA) acquisition areas on commercial devices are 3x3- or 6x6-mm. Compared to 3x3-mm angiograms with proper sampling density, 6x6-mm angiograms have significantly lower scan quality, with reduced signal-to-noise ratio and worse shadow artifacts due to undersampling. Here, we propose a deep-learning-based high-resolution angiogram reconstruction network (HARNet) to generate enhanced 6x6-mm superficial vascular complex (SVC) angiograms. The network was trained on data from 3x3-mm and 6x6-mm angiograms from the same eyes. The reconstructed 6x6-mm angiograms have significantly lower noise intensity and better vascular connectivity than the original images. The algorithm did not generate false flow signal at the noise level presented by the original angiograms. The image enhancement produced by our algorithm may improve biomarker measurements and qualitative clinical assessment of 6x6-mm OCTA.

eess.IV↗

arXiv2020

Automated segmentation of retinal fluid volumes from structural and angiographic optical coherence tomography using deep learning

Purpose: We proposed a deep convolutional neural network (CNN), named Retinal Fluid Segmentation Network (ReF-Net) to segment volumetric retinal fluid on optical coherence tomography (OCT) volume. Methods: 3 x 3-mm OCT scans were acquired on one eye by a 70-kHz OCT commercial AngioVue system (RTVue-XR; Optovue, Inc.) from 51 participants in a clinical diabetic retinopathy (DR) study (45 with retinal edema and 6 healthy controls). A CNN with U-Net-like architecture was constructed to detect and segment the retinal fluid. Cross-sectional OCT and angiography (OCTA) scans were used for training and testing ReF-Net. The effect of including OCTA data for retinal fluid segmentation was investigated in this study. Volumetric retinal fluid can be constructed using the output of ReF-Net. Area-under-Receiver-Operating-Characteristic-curve (AROC), intersection-over-union (IoU), and F1-score were calculated to evaluate the performance of ReF-Net. Results: ReF-Net shows high accuracy (F1 = 0.864 +/- 0.084) in retinal fluid segmentation. The performance can be further improved (F1 = 0.892 +/- 0.038) by including information from both OCTA and structural OCT. ReF-Net also shows strong robustness to shadow artifacts. Volumetric retinal fluid can provide more comprehensive information than the 2D area, whether cross-sectional or en face projections. Conclusions: A deep-learning-based method can accurately segment retinal fluid volumetrically on OCT/OCTA scans with strong robustness to shadow artifacts. OCTA data can improve retinal fluid segmentation. Volumetric representations of retinal fluid are superior to 2D projections. Translational Relevance: Using a deep learning method to segment retinal fluid volumetrically has the potential to improve the diagnostic accuracy of diabetic macular edema by OCT systems.

eess.IV↗

arXiv2020

High-resolution wide-field OCT angiography with a self-navigation method to correct microsaccades and blinks

In this study, we demonstrate a novel self-navigated motion correction method that suppresses eye motion and blinking artifacts on wide-field optical coherence tomographic angiography (OCTA) without requiring any hardware modification. Highly efficient GPU-based, real-time OCTA image acquisition and processing software was developed to detect eye motion artifacts. The algorithm includes an instantaneous motion index that evaluates the strength of motion artifact on en face OCTA images. Areas with suprathreshold motion and eye blinking artifacts are automatically rescanned in real-time. Both healthy eyes and eyes with diabetic retinopathy were imaged, and the self-navigated motion correction performance was demonstrated.

physics.med-ph↗