https://orcid.org/0000-0001-8579-7423
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ABSTRACT
The inverse problem associated with Diffuse optical tomography image reconstruction is known to be highly nonlinear, under-determined, and ill-posed. The Levenberg-Marquardt technique is employed in solving it and is known to produce low-resolution reconstructed images. To stabilize the inversion of the large matrix, a heuristically chosen regularization parameter is used. A novel methodology is developed using Gauss-Seidel, Modified Richardson, and Kaczmarz recursive methods to solve the inverse problem and to obtain spatially varying regularization parameters, which are optimally obtained for every node automatically, which is otherwise not possible. The proposed methods are thoroughly compared with the existing traditional methods in both 2-D and 3-D imaging domains using numerically simulated noisy data and also real-life phantom data. Of all the proposed methods, the Gauss-Seidel-based method provides a quantitatively accurate estimation of spatially varying regularization using the model-resolution-matrix-based method and hence improves the quality of the reconstructed images with better resolution characteristics.
Code and data availability statement
Upon a reasonable request, Code and Data will be made available.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Additional information
Notes on contributors
Harish G. Siddalingaiah
Harish G. Siddalingaiah obtained his M.Tech degree from Siddaganga Institute of Technology, Tumkur, India. Currently, he is a Ph.D. research scholar at the Department of Electronics and Communication Engineering, National Institute of Technology Goa, Goa, India. His research areas include Bio-medical Imaging, Inverse problems, and Numerical Optimization.
Ravi Prasad K. Jagannath
Ravi Prasad K. Jagannath obtained his Ph.D. degree from the Indian Institute of Science, Bangalore, India in 2014. Currently, he is an associate professor of Mathematics at the Department of Applied Sciences, National Institute of Technology Goa, Goa, India. He has authored many research papers in various journals and conferences. His research areas include Bio-medical Imaging, Inverse problems, and Numerical Optimization.
Gurusiddappa R. Prashanth
Gurusiddappa R. Prashanth obtained his Ph.D. degree from the Indian Institute of Science, Bangalore, India in 2014. Currently, he is an associate professor at the Department of Electronics and Communication Engineering, National Institute of Technology Goa, Goa, India. He has authored many research papers in various journals and conferences. His research areas include the development of low-cost point-of-care diagnostics, Bio-photonics, Bio-sensors, and Bio-medical Imaging.