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Nonlinear parametric inverse problems appear in many applications. Here, we focus on diffuse optical tomography (DOT) in medical imaging to recover unknown images of interest, such as cancerous tissue in a given medium, using a mathematical…

Numerical Analysis · Mathematics 2020-07-14 Selin Aslan , Eric de Sturler , Serkan Gugercin

In nonlinear imaging problems whose forward model is described by a partial differential equation (PDE), the main computational bottleneck in solving the inverse problem is the need to solve many large-scale discretized PDEs at each step of…

Numerical Analysis · Mathematics 2016-03-08 Meghan O'Connell , Misha E. Kilmer , Eric de Sturler , Serkan Gugercin

When the inverse problem of diffuse optical tomography (DOT) is solved with the Born or Rytov approximation, the size of the matrix of the linear inverse problem becomes large if the volume (or area) of the domain in biological tissue used…

Medical Physics · Physics 2021-07-22 Tetsuya Mimura , Yu Jiang , Norikazu Todoroki , Manabu Machida

Diffuse optical tomography (DOT) utilises near-infrared light for imaging spatially distributed optical parameters, typically the absorption and scattering coefficients. The image reconstruction problem of DOT is an ill-posed inverse…

Computational Physics · Physics 2021-12-15 Meghdoot Mozumder , Andreas Hauptmann , Ilkka Nissilä , Simon R. Arridge , Tanja Tarvainen

Medical imaging is nowadays a pillar in diagnostics and therapeutic follow-up. Current research tries to integrate established - but ionizing - tomographic techniques with technologies offering reduced radiation exposure. Diffuse Optical…

Numerical Analysis · Mathematics 2024-02-15 Alessandro Benfenati , Paola Causin , Martina Quinteri

Diffuse optical tomography (DOT) has been investigated as an alternative imaging modality for breast cancer detection thanks to its excellent contrast to hemoglobin oxidization level. However, due to the complicated non-linear photon…

Computer Vision and Pattern Recognition · Computer Science 2019-09-10 Jaejun Yoo , Sohail Sabir , Duchang Heo , Kee Hyun Kim , Abdul Wahab , Yoonseok Choi , Seul-I Lee , Eun Young Chae , Hak Hee Kim , Young Min Bae , Young-wook Choi , Seungryong Cho , Jong Chul Ye

Nonlinear parametric inverse problems appear in several prominent applications; one such application is Diffuse Optical Tomography (DOT) in medical image reconstruction. Such inverse problems present huge computational challenges, mostly…

A two-step shape reconstruction method for diffuse optical tomography (DOT) is presented which uses adjoint fields and level sets. The propagation of near-infrared photons in tissue is modeled by the time-dependent linear transport…

Numerical Analysis · Mathematics 2025-10-20 Oliver Dorn

In fluorescence diffuse optical tomography (fDOT), the reconstruction of the fluorophore concentration inside the target body is usually carried out using a normalized Born approximation model where the measured fluorescent emission data is…

Computational Physics · Physics 2015-01-05 Meghdoot Mozumder , Tanja Tarvainen , Simon Arridge , Jari P. Kaipio , Cosimo d'Andrea , Ville Kolehmainen

Diffuse optical breast imaging utilizes near-infrared (NIR) light propagation through tissues to assess the optical properties of tissue for the identification of abnormal tissue. This optical imaging approach is sensitive, cost-effective,…

Medical Physics · Physics 2017-11-22 Wenxiang Cong , Xavier Intes , Ge Wang

The inverse source problem arising in photoacoustic tomography and in several other coupled-physics modalities is frequently solved by iterative algorithms. Such algorithms are based on the minimization of a certain cost functional. In…

Image and Video Processing · Electrical Eng. & Systems 2025-10-29 Andreas Hauptmann , Leonid Kunyansky , Jenni Poimala

A deep learning-assisted inversion method is proposed to solve the inhomogeneous background imaging problem. Three non-iterative methods, namely the distorted-Born (DB) major current coefficients method, the DB modified Born approximation…

Applied Physics · Physics 2023-12-12 Naike Du , Tiantian Yin , Jing Wang , Rencheng Song , Kuiwen Xu , Bingyuan Liang , Sheng Sun , Xiuzhu Ye

Time harmonic inverse scattering using accurate forward models is often computationally expensive. On the other hand, the use of computationally efficient solvers, such as the Born approximation, may fail if the targets do not satisfy the…

Computational Physics · Physics 2019-07-05 Jari P. Kaipio , Tomi Huttunen , Teemu Luostari , Timo Lähivaara , Peter B. Monk

Diffuse optical tomography (DOT) is an imaging modality which uses near-infrared light. Although iterative numerical schemes are commonly used for its inverse problem, correct solutions are not obtained unless good initial guesses are…

Numerical Analysis · Mathematics 2021-06-07 Yu Jiang , Manabu Machida , Norikazu Todoroki

The Diffuse Optical Tomography (DOT) has received considerable attention in the recent years in the field of biomedical imaging and disease detection. However, imaging through highly diffusive medium is a challenge and stability is always…

Image and Video Processing · Electrical Eng. & Systems 2020-03-31 Tapan Das , P. K. Dutta

In this paper, we formulate the reconstruction problem in diffuse optical tomography (DOT) in a statistical setting for determining the optical parameters, scattering and absorption, from boundary photon density measurements. A special kind…

Numerical Analysis · Mathematics 2020-02-20 Thilo Strauss , Sanwar Ahmad , Taufiquar Khan

Inverse boundary value problems for the radiative transport equation play important roles in optics-based medical imaging techniques such as diffuse optical tomography (DOT) and fluorescence optical tomography (FOT). Despite the rapid…

Numerical Analysis · Mathematics 2015-06-19 Tian Ding , Kui Ren

We introduce a novel algorithm for nonlinear processing of data gathered by an active array of sensors which probes a medium with pulses and measures the resulting waves. The algorithm is motivated by the application of array imaging. We…

Numerical Analysis · Mathematics 2019-02-20 Liliana Borcea , Vladimir Druskin , Alexander V. Mamonov , Mikhail Zaslavsky

Nonlinear parametric inverse problems appear in many applications and are typically very expensive to solve, especially if they involve many measurements. These problems pose huge computational challenges as evaluating the objective…

Numerical Analysis · Mathematics 2020-03-25 Drayton Munster , Eric de Sturler

Diffuse Optical Tomography (DOT) is an emerging technology in medical imaging which employs light in the NIR spectrum to estimate the distribution of optical coefficients in biological tissues for diagnostic and monitoring purposes. DOT…

Numerical Analysis · Mathematics 2022-05-27 Alessandro Benfenati , Giuseppe Bisazza , Paola Causin
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