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Full-Text Articles in Physical Sciences and Mathematics
Uniqueness Theorems In Bioluminescence Tomography, Ge Wang, Yi Li, Ming Jiang
Uniqueness Theorems In Bioluminescence Tomography, Ge Wang, Yi Li, Ming Jiang
Mathematics and Statistics Faculty Publications
Motivated by bioluminescent imaging needs for studies on gene therapy and other applications in the mouse models, a bioluminescence tomography (BLT) system is being developed in the University of Iowa. While the forward imaging model is described by the well-known diffusion equation, the inverse problem is to recover an internal bioluminescent source distribution subject to Cauchy data. Our primary goal in this paper is to establish the solution uniqueness for BLT under practical constraints despite the ill-posedness of the inverse problem in the general case. After a review on the inverse source literature, we demonstrate that in the general case …
The Dual Spectral Set Conjecture, Steen Pedersen
The Dual Spectral Set Conjecture, Steen Pedersen
Mathematics and Statistics Faculty Publications
Suppose that Λ = (aZ + b) ∪ (cZ + d) where a, b, c, d are real numbers such that a ≠ 0 and c ≠ 0. The union is not assumed to be disjoint. It is shown that the translates Ω + λ, λ is an element of Λ, tile the real line for some bounded measurable set Ω if and only if the exponentials eλ(x) = ei2πλx, λ is an element of Λ, form an orthogonal basis for some bounded measurable set Ω'.