Uncertainty Principles for Inverse Source Problems, Far Field Splitting, and Data Completion
نویسندگان
چکیده
منابع مشابه
Uncertainty Principles for Inverse Source Problems, Far Field Splitting, and Data Completion
The next lemma shows that odd and even rescaled squared singular values, sn(R), are monotonically decreasing for n ≥ 0 and monotonically increasing for n ≤ 0. ∗Submitted to the editors July 22, 2016. †Institut für Mathematik, Universität Würzburg, 97074 Würzburg, Germany ([email protected]). ‡Department of Mathematics, University of Washington, Seattle, Washington 98195, U.S.A....
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در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...
Far Field Splitting
The aim of far field splitting for time-harmonic acoustic or electromagnetic waves is to decompose the far field of a wave radiated by an ensemble of several compactly supported sources into the individual far field components radiated by each of these sources separately. Without further assumptions this is an ill-posed inverse problem. Observing that far fields radiated by compactly supported ...
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Given far field data of a time-harmonic wave radiated by an ensemble of well separated acoustic or electromagnetic sources as well as a priori information on the locations of these sources, we discuss an algorithm to approximate the far field data radiated by each of these sources separately. The method is based on a Galerkin procedure considering subspaces spanned by the singular vectors of “r...
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The time-dependent inverse source problem with far-field data is investigated within a limited-view Radon inversion framework, analogous to that of a limited-view computed tomography reconstruction problem. We investigate the domains in the Radon and Fourier spaces within which data are available for the reconstruction of the space–time structure of the source. Using a linear inversion formalis...
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ژورنال
عنوان ژورنال: SIAM Journal on Applied Mathematics
سال: 2017
ISSN: 0036-1399,1095-712X
DOI: 10.1137/16m1086157