1,144 research outputs found
Real-time diffuse optical tomography using reduced-order light propagation models based on a priori anatomical and functional information
This paper proposes a new fast 3D image reconstruction
algorithm for Diffuse Optical Tomography using reduced
order polynomial mappings from the space of optical
tissue parameters into the space of flux measurements at
the detector locations. The polynomial mappings are
constructed through an iterative estimation process
involving structure detection, parameter estimation and
cross-validation using data generated by simulating a
diffusion approximation of the radiative transfer equation
incorporating a priori anatomical and functional
information provided by MR scans and prior psychological
evidence. Numerical simulation studies demonstrate that
reconstructed images are remarkably similar in quality as
those obtained using the standard approach, but obtained at
a fraction of the time
EIT Reconstruction Algorithms: Pitfalls, Challenges and Recent Developments
We review developments, issues and challenges in Electrical Impedance
Tomography (EIT), for the 4th Workshop on Biomedical Applications of EIT,
Manchester 2003. We focus on the necessity for three dimensional data
collection and reconstruction, efficient solution of the forward problem and
present and future reconstruction algorithms. We also suggest common pitfalls
or ``inverse crimes'' to avoid.Comment: A review paper for the 4th Workshop on Biomedical Applications of
EIT, Manchester, UK, 200
Characterizing Accuracy of Total Hemoglobin Recovery Using Contrast-Detail Analysis in 3D Image-Guided Near Infrared Spectroscopy with the Boundary Element Method
The quantification of total hemoglobin concentration (HbT) obtained from multi-modality image-guided near infrared spectroscopy (IG-NIRS) was characterized using the boundary element method (BEM) for 3D image reconstruction. Multi-modality IG-NIRS systems use a priori information to guide the reconstruction process. While this has been shown to improve resolution, the effect on quantitative accuracy is unclear. Here, through systematic contrast-detail analysis, the fidelity of IG-NIRS in quantifying HbT was examined using 3D simulations. These simulations show that HbT could be recovered for medium sized (20mm in 100mm total diameter) spherical inclusions with an average error of 15%, for the physiologically relevant situation of 2:1 or higher contrast between background and inclusion. Using partial 3D volume meshes to reduce the ill-posed nature of the image reconstruction, inclusions as small as 14mm could be accurately quantified with less than 15% error, for contrasts of 1.5 or higher. This suggests that 3D IG-NIRS provides quantitatively accurate results for sizes seen early in treatment cycle of patients undergoing neoadjuvant chemotherapy when the tumors are larger than 30mm
Uniqueness, Born Approximation, and Numerical Methods for Diffuse Optical Tomography
Diffuse optical tomogrpahy (DOT) is to find optical coefficients of tissue using near infrared light. DOT as an inverse problem is described and the studies about unique determination of optical coefficients are summarized. If a priori information of the optical coefficient is known, DOT is reformulated to find a perturbation of the optical coefficients inverting the Born expansion which is an infinite series expansion with respect to the perturbation and the a priori information. Numerical methods for DOT are explained as methods inverting first- or second-order Born approximation or the Born expansion itself
Fast and efficient image reconstruction for high density diffuse optical imaging of the human brain
Real-time imaging of human brain has become an important technique within neuroimaging. In this study, a fast and efficient sensitivity map generation based on Finite Element Models (FEM) is developed which utilises a reduced sensitivitys matrix taking advantage of sparsity and parallelisation processes. Time and memory efficiency of these processes are evaluated and compared with conventional method showing that for a range of mesh densities from 50000 to 320000 nodes, the required memory is reduced over tenfold and computational time fourfold allowing for near real-time image recovery
Transformer Meets Boundary Value Inverse Problems
A Transformer-based deep direct sampling method is proposed for a class of
boundary value inverse problems. A real-time reconstruction is achieved by
evaluating the learned inverse operator between carefully designed data and the
reconstructed images. An effort is made to give a specific example to a
fundamental question: whether and how one can benefit from the theoretical
structure of a mathematical problem to develop task-oriented and
structure-conforming deep neural networks? Specifically, inspired by direct
sampling methods for inverse problems, the 1D boundary data in different
frequencies are preprocessed by a partial differential equation-based feature
map to yield 2D harmonic extensions as different input channels. Then, by
introducing learnable non-local kernels, the direct sampling is recast to a
modified attention mechanism. The proposed method is then applied to electrical
impedance tomography, a well-known severely ill-posed nonlinear inverse
problem. The new method achieves superior accuracy over its predecessors and
contemporary operator learners, as well as shows robustness with respect to
noise. This research shall strengthen the insights that the attention
mechanism, despite being invented for natural language processing tasks, offers
great flexibility to be modified in conformity with the a priori mathematical
knowledge, which ultimately leads to the design of more physics-compatible
neural architectures
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