scholarly journals Regularization of the Factorization Method applied to diffuse optical tomography

2021 ◽  
Author(s):  
Isaac Harris
Keyword(s):  
A Priori ◽  
Optical Tomography ◽  
Diffuse Optical Tomography ◽  
Singular Values ◽  
Factorization Method ◽  
Complex Hilbert Space ◽  
Two Dimensions ◽  
Numerical Instabilities ◽  
Priori Information ◽  
Unknown Region

Abstract In this paper, we develop a new regularized version of the Factorization Method for positive operators mapping a complex Hilbert Space into it’s dual space. The Factorization Method uses Picard’s Criteria to define an indicator function to image an unknown region. In most applications the data operator is compact which gives that the singular values can tend to zero rapidly which can cause numerical instabilities. The regularization of the Factorization Method presented here seeks to avoid the numerical instabilities in applying Picard’s Criteria. This method allows one to image the interior structure of an object with little a priori information in a computationally simple and analytically rigorous way. Here we will focus on an application of this method to diffuse optical tomography where will prove that this method can be used to recover an unknown subregion from the Dirichlet-to-Neumann mapping. Numerical examples will be presented in two dimensions.

scholarly journals Optimal Analysis Method for Dynamic Contrast-Enhanced Diffuse Optical Tomography

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Michael Ghijsen ◽  
Yuting Lin ◽  
Mitchell Hsing ◽  
Orhan Nalcioglu ◽  
Gultekin Gulsen
Keyword(s):  
Spatial Resolution ◽  
Animal Studies ◽  
Imaging Modality ◽  
A Priori ◽  
Optical Tomography ◽  
Diffuse Optical Tomography ◽  
Dynamic Contrast Enhanced ◽  
Promising Tool ◽  
Reconstruction Methods ◽  
Contrast Enhanced

Diffuse Optical Tomography (DOT) is an optical imaging modality that has various clinical applications. However, the spatial resolution and quantitative accuracy of DOT is poor due to strong photon scatting in biological tissue. Structurala prioriinformation from another high spatial resolution imaging modality such as Magnetic Resonance Imaging (MRI) has been demonstrated to significantly improve DOT accuracy. In addition, a contrast agent can be used to obtain differential absorption images of the lesion by using dynamic contrast enhanced DOT (DCE-DOT). This produces a relative absorption map that consists of subtracting a reconstructed baseline image from reconstructed images in which optical contrast is included. In this study, we investigated and compared different reconstruction methods and analysis approaches for regular endogenous DOT and DCE-DOT with and without MR anatomicala prioriinformation for arbitrarily-shaped objects. Our phantom and animal studies have shown that superior image quality and higher accuracy can be achieved using DCE-DOT together with MR structurala prioriinformation. Hence, implementation of a combined MRI-DOT system to image ICG enhancement can potentially be a promising tool for breast cancer imaging.

TH-D-M100J-02: Quantitative Interstitial Multispectral Diffuse Optical Tomography of Human Prostate Using a Priori Structure Information

2007 ◽  
Vol 34 (6Part23) ◽  
pp. 2638-2638
Author(s):  
X Zhou ◽  
T Zhu ◽  
J Finlay ◽  
J Li ◽  
A Dimofte ◽  
...  
Keyword(s):  
A Priori ◽  
Optical Tomography ◽  
Diffuse Optical Tomography ◽  
Human Prostate ◽  
Structure Information

Inversion of inductive electromagnetic data in highly conductive terrains

Geophysics ◽  
2005 ◽  
Vol 70 (1) ◽  
pp. G16-G28 ◽  
Author(s):  
G. Schultz ◽  
C. Ruppel
Keyword(s):  
A Priori ◽  
Two Dimensions ◽  
Forward Model ◽  
Practical Applications ◽  
Shallow Subsurface ◽  
Subsurface Structures ◽  
Conductivity Structure ◽  
Actual Field ◽  
Priori Information ◽  
The Stability

Despite the increasing use of controlled-source frequency-domain EM data to characterize shallow subsurface structures, relatively few inversion algorithms have been widely applied to data from real-world settings, particularly in high-conductivity terrains. In this study, we develop robust and convergent regularized, least-squares inversion algorithms based on both linear and nonlinear formulations of mutual dipole induction for the forward problem. A modified version of the discrepancy principle based on a priori information is implemented to select optimal smoothing parameters that simultaneously guarantee the stability and best-fit criteria. To investigate the problems of resolution and equivalence, we consider typical layered-earth models in one and two dimensions using both synthetic and observed data. Synthetic examples show that inversions based on the nonlinear forward model more accurately resolve subsurface structure, and that inversions based on the linear forward model tend to drastically underpredict high conductivities at depth. Inversions of actual field data from well-characterized sites (e.g., National Geotechnical Experimentation Site; sand-dominated coastal aquifer in the Georgia Bight) are used to test the applicability of the model to terrains with different characteristic conductivity structure. A comparison of our inversion results with existing cone-penetrometer and downhole-conductivity data from these field sites demonstrates the ability of the inversions to constrain conductivity variations in practical applications.

scholarly journals Diffuse optical tomography with a priori anatomical information

2005 ◽  
Vol 50 (12) ◽  
pp. 2837-2858 ◽  
Author(s):  
Murat Guven ◽  
Birsen Yazici ◽  
Xavier Intes ◽  
Britton Chance
Keyword(s):  
A Priori ◽  
Optical Tomography ◽  
Diffuse Optical Tomography ◽  
Anatomical Information

Fluorescence optical tomography with a priori information

2007 ◽  
Author(s):  
Murat Guven ◽  
Birsen Yazici ◽  
Vasilis Ntziachristos
Keyword(s):  
A Priori ◽  
Optical Tomography ◽  
A Priori Information ◽  
Priori Information
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