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Fundamental Light–Tissue Interactions: Light Scattering and Absorption
Published in Vadim Backman, Adam Wax, Hao F. Zhang, A Laboratory Manual in Biophotonics, 2018
Vadim Backman, Adam Wax, Hao F. Zhang
While solving the direct scattering problem is difficult, the inverse scattering problem is even more complex. It deals with learning about tissue structure (e.g., measurement of ρ(r)) based on an experimentally measured f(s,s0). In practice, the complete function f(s,s0) is never known, which further complicates the problem. Interest in these inverse scattering problems stems from the fact that it is comparatively easy to make light-scattering measurements either on excised or living tissue: The method is nondistractive and does not require cumbersome preparation as would be required for, as an example, electron microscopy. In tissue optics, inverse problems are typically solved by the use of physical approximations that relate ρ(r) and particular scattering characteristics that are observed in an experiment. In this section, some of the relevant approximations are discussed.
A brief introduction to inverse scattering theory
Published in C Constanda, J Saranen, S Seikkala, Integral methods in science and engineering, 2020
Unfortunately, from the point of view of applications, the inverse scattering problem is improperly posed in the sense that the solution does not depend continuously on the data! Furthermore, the problem is non-linear (for example, if ∂D is described by x = r(x^)x^, r(x^) > 0, then u∞ is not a linear function of r(x^)). Hence, the usual approach to solving the inverse scattering problem is through nonlinear optimisation methods using regularisation techniques (cf. [1] and [10]). Here we will briefly describe a new method, which avoids non-linear optimisation techniques [11]. (For a somewhat related method, see [12]). In what follows, we need only assume that λ ≥ 0, and do not need to know λ precisely, i.e., in contrast to nonlinear optimization methods we do not need to know the boundary condition! The method we propose is based on the following theorem, where we write x^ = (cos θ, sin θ), d = (cos α, sin α), u∞(x^, d) = u∞(θ, α), g(d) = g(α) ∊ L2(−π, π), and y0 = (ρ cos φ, ρ sin φ) is assumed to be a point in D.
Virtual Experiments and Compressive Sensing for Subsurface Microwave Tomography
Published in C.H. Chen, Compressive Sensing of Earth Observations, 2017
Martina Bevacqua, Lorenzo Crocco, Loreto Di Donato, Tommaso Isernia, Roberta Palmeri
The inverse scattering problem amounts to retrieve the unknown contrast function, which encodes the geometrical and electromagnetic properties of the targets, solving the couple of Equations 8.1 and 8.2 for given incident fields and corresponding (measured) scattered fields.
Forward scattering for non-linear wave propagation in (3 + 1)-dimensional Jimbo-Miwa equation using singular manifold and group transformation methods
Published in Waves in Random and Complex Media, 2022
Ahmed S. Rashed, Samah M. Mabrouk, Abdul-Majid Wazwaz
Scattering theory has a profound impact on studying and understanding the scattering waves in engineering mathematics and physical applications [1]. Direct scattering problem deals with the distribution determination of the scattered flux basing on its https://en.wikipedia.org/wiki/Scattering characteristics. Inverse scattering problem deals with the determination of the flux characteristics. Inverse scattering transformation (IST) has been extensively studied in the engineering, physical and mathematical communities, last decades [1–4]. Forward scattering is the major step in IST, it mainly depends on finding the Lax pair.