Graph- and finite element-based total variation models for the inverse problem in diffuse optical tomography

Lu, Wenqi; Duan, Jinming; David, Olivier; Hervé, Lionel; Styles, Iain B.

doi:10.1364/boe.10.002684

Cited by 30 publications

(26 citation statements)

References 53 publications

(78 reference statements)

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“…In this paper, we build the graph by using the positions of the nodes and the connectivity between nodes in the finite element mesh as the vertices and edges in the graph to sparsify the graph for computational efficiency. We have learned from previous work [8] that the graph-based nonlocal inverse model with this sparse method can achieve accurate and stable reconstruction, regardless of the mesh resolution. Therefore for each vertex i, we consider only those vertices that are directly connected to the vertex i for N i (i.e.…”

Section: Methodsmentioning

confidence: 99%

“…We denote ∇ w (·), div w (·) and N w (·) as the nonlocal gradient, the nonlocal divergence and the nonlocal normal derivative, respectively. Their definitions are given in Equations (6), (7) and (8). We simply replace the differential operators in Equation (1) with their nonlocal counterparts and solve the new NDE under the framework of nonlocal vector calculus:…”

Section: Methodsmentioning

confidence: 99%

“…However, FEM implementations can be difficult and timeconsuming, especially when higher-order polynomial basis (shape) functions are used for non-linear interpolation between vertices of high-order elements [7]. In previous work [8], we introduced a graph representation to discretize a totalvariation regularization term for the inverse problem in DOT. In this discretization, the object geometry is represented by an unstructured graph, defined by vertices, edges and weights.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

New nonlocal forward model for diffuse optical tomography

Duan

Veesa

et al. 2019

Biomed. Opt. Express

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The forward model in diffuse optical tomography (DOT) describes how light propagates through a turbid medium. It is often approximated by a diffusion equation (DE) that is numerically discretized by the classical finite element method (FEM). We propose a nonlocal diffusion equation (NDE) as a new forward model for DOT, the discretization of which is carried out with an efficient graph-based numerical method (GNM). To quantitatively evaluate the new forward model, we first conduct experiments on a homogeneous slab, where the numerical accuracy of both NDE and DE is compared against the existing analytical solution. We further evaluate NDE by comparing its image reconstruction performance (inverse problem) to that of DE. Our experiments show that NDE is quantitatively comparable to DE and is up to 64% faster due to the efficient graph-based representation that can be implemented identically for geometries in different dimensions.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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New nonlocal forward model for diffuse optical tomography

Duan

Veesa

et al. 2019

Biomed. Opt. Express

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“…It is a non-local method because it uses patch similarity formulation (i.e. Gaussian kernel function), which is inspired by the non-local methods used in image denoising [31], inpainting [32], [33] and reconstruction [34]. It has been shown in [35] that, in a Bayesian framework, (5) is essentially a weighted K nearest neighbours ( KNN ) classifier, which determines the label by maximum likelihood estimation.…”

Section: Methodsmentioning

confidence: 99%

Automatic 3D Bi-Ventricular Segmentation of Cardiac Images by a Shape-Refined Multi- Task Deep Learning Approach

Duan

Bello

Schlemper

et al. 2019

IEEE Trans. Med. Imaging

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197

109

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Deep learning approaches have achieved state-of-the-art performance in cardiac magnetic resonance (CMR) image segmentation. However, most approaches have focused on learning image intensity features for segmentation, whereas the incorporation of anatomical shape priors has received less attention. In this paper, we combine a multi-task deep learning approach with atlas propagation to develop a shape-refined bi-ventricular segmentation pipeline for short-axis CMR volumetric images. The pipeline first employs a fully convolutional network (FCN) that learns segmentation and landmark localisation tasks simultaneously. The architecture of the proposed FCN uses a 2.5D representation, thus combining the computational advantage of 2D FCNs networks and the capability of addressing 3D spatial consistency without compromising segmentation accuracy. Moreover, a refinement step is designed to explicitly impose shape prior knowledge and improve segmentation quality. This step is effective for overcoming image artefacts (e.g. due to different breath-hold positions and large slice thickness), which preclude the creation of anatomically meaningful 3D cardiac shapes. The pipeline is fully automated, due to network’s ability to infer landmarks, which are then used downstream in the pipeline to initialise atlas propagation. We validate the pipeline on 1831 healthy subjects and 649 subjects with pulmonary hypertension. Extensive numerical experiments on the two datasets demonstrate that our proposed method is robust and capable of producing accurate, high-resolution and anatomically smooth bi-ventricular 3D models, despite the presence of artefacts in input CMR volumes.

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“…But on the trail, they are walking, nature does not give any better opportunity to take progressive steps. Hence, they have changed their focus into mathematical short‐cut methods 13‐32 …”

Section: Introductionmentioning

confidence: 99%

Differential photon waves imaging

Kazancı

2020

Int J Imaging Syst Tech

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Imaging philosophy was simulated for well‐known biomedical diffuse optical imaging (DOI) methodology. It runs based on the differential photon waves. The underlying philosophy of imaging methodology takes its origin from the distance of the same molecule types. Inherently, each type of biological molecules has different molecular structure, size, and binding distance. Molecules might be water, oxy‐hemoglobin, deoxyhemoglobin, ATP, pepsin, cholesterol, protein, fats or lipids, hydroxyapatite, carbohydrates, glucose, glycogen, DNA, etc. These molecules need to be grouped for biomedical photon imaging purposes such as in hair, skull, scalp, cortex, dermis, epidermis, cerebrospinal fluid, cerebellar gray and white matter for neuroimaging; or skin, fat, water for breast imaging; optic nerve, humor aqueous for eye imaging; bones and joints for skeletal system imaging; liver, muscle, fibroadenoma breast, mucous tissue, nodule, bowel, heart, kidneys, lung, stomach, whole blood vascular system for inner organs. Among these different types of molecular structures, each type has different characteristic photon absorption and scattering coefficients for corresponding wavelength. Researchers have been using these characteristic wavelengths to reconstruct the images. They have focused on either absorption or scattering maximums of specific wavelengths for each tissue type. This is right when the molecules are investigated first, but it is a dead‐end when it goes deep tissue, since low‐power laser photons scatter randomly when they penetrate inside the tissue, immediately. Novel approach uses phase‐shifted group photon waves corresponding to the molecular distances. Single photon wavelength can be used to investigate the molecules inside the imaging media.

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Graph- and finite element-based total variation models for the inverse problem in diffuse optical tomography

Cited by 30 publications

References 53 publications

New nonlocal forward model for diffuse optical tomography

New nonlocal forward model for diffuse optical tomography

Automatic 3D Bi-Ventricular Segmentation of Cardiac Images by a Shape-Refined Multi- Task Deep Learning Approach

Differential photon waves imaging

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