Zobrazeno 1 - 10
of 28
pro vyhledávání: '"GIOVANNI S. ALBERTI"'
Publikováno v:
Mathematics in Engineering, Vol 2, Iss 2, Pp 264-286 (2020)
In this paper we introduce the randomised stability constant for abstract inverse problems, as a generalisation of the randomised observability constant, which was studied in the context of observability inequalities for the linear wave equation. We
Externí odkaz:
https://doaj.org/article/8c3f978d2b944b189250fe135681d8fc
Publikováno v:
Forum of Mathematics, Sigma, Vol 7 (2019)
We prove that an $L^{\infty }$ potential in the Schrödinger equation in three and higher dimensions can be uniquely determined from a finite number of boundary measurements, provided it belongs to a known finite dimensional subspace ${\mathcal{W}}$.
Externí odkaz:
https://doaj.org/article/be155b7c4f2b46c6aa70bb1b877ece41
Publikováno v:
Nonlinearity. 36:734-808
We consider abstract inverse problems between infinite-dimensional Banach spaces. These inverse problems are typically nonlinear and ill-posed, making the inversion with limited and noisy measurements a delicate process. In this work, we assume that
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0422418dd6487074531463db86c892bb
https://doi.org/10.1088/1361-6544/aca73d
https://doi.org/10.1088/1361-6544/aca73d
Publikováno v:
Applied and Computational Harmonic Analysis. 50:105-146
We consider a compressed sensing problem in which both the measurement and the sparsifying systems are assumed to be frames (not necessarily tight) of the underlying Hilbert space of signals, which may be finite or infinite dimensional. The main resu
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cddfdd9e53296fb9664e26a5535e6497
https://doi.org/10.1016/j.acha.2019.08.002
https://doi.org/10.1016/j.acha.2019.08.002
Publikováno v:
Applicable Analysis. 101:3636-3654
We prove a local Lipschitz stability estimate for Gel'fand-Calder\'on's inverse problem for the Schr\"odinger equation. The main novelty is that only a finite number of boundary input data is available, and those are independent of the unknown potent
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::61637d4f0b9d4a703c325edb44976f9c
https://doi.org/10.1080/00036811.2020.1745192
https://doi.org/10.1080/00036811.2020.1745192
Autor:
Giovanni S. Alberti
Publikováno v:
Inverse Problems. 38:124005
Hybrid inverse problems are based on the interplay of two types of waves, in order to allow for imaging with both high resolution and high contrast. The inversion procedure often consists of two steps: first, internal measurements involving the unkno
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a2e588cb0e0ae720e235b2024646384b
https://doi.org/10.1088/1361-6420/ac9924
https://doi.org/10.1088/1361-6420/ac9924
Publikováno v:
Landscapes of Time-Frequency Analysis ISBN: 9783030560041
We illustrate the general point of view we developed in an earlier paper (SIAM J. Math. Anal., 2019) that can be described as a variation of Helgason’s theory of dual G-homogeneous pairs (X, Ξ ) and which allows us to prove intertwining properties
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d437472885d2a0f7b54d2c9d0c52bbdb
https://doi.org/10.1007/978-3-030-56005-8_1
https://doi.org/10.1007/978-3-030-56005-8_1
Publikováno v:
Mathematics in Engineering
Mathematics in Engineering, AIMS, 2020, 2 (2), pp.264-286. ⟨10.3934/mine.2020013⟩
Mathematics in Engineering, 2020, 2 (2), pp.264-286. ⟨10.3934/mine.2020013⟩
Mathematics in Engineering, Vol 2, Iss 2, Pp 264-286 (2020)
Mathematics in Engineering, AIMS, 2020, 2 (2), pp.264-286. ⟨10.3934/mine.2020013⟩
Mathematics in Engineering, 2020, 2 (2), pp.264-286. ⟨10.3934/mine.2020013⟩
Mathematics in Engineering, Vol 2, Iss 2, Pp 264-286 (2020)
International audience; In this paper we introduce the randomised stability constant for abstract inverse problems, as a generalisation of the randomised observability constant, which was studied in the context of observability inequalities for the l
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2ff7cadb131f6bc90ecaff13b4165090
http://hdl.handle.net/11567/998955
http://hdl.handle.net/11567/998955
We present a general framework to study uniqueness, stability and reconstruction for infinite-dimensional inverse problems when only a finite-dimensional approximation of the measurements is available. For a large class of inverse problems satisfying
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e6cc17ce1421ffe70bcb7c2245d955eb
http://arxiv.org/abs/1906.10028
http://arxiv.org/abs/1906.10028
We consider the dynamical superresolution problem consisting in the recovery of positions and velocities of moving particles from low-frequency static measurements taken over multiple time steps. T...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::08f12d93621a2d1b43f64cb97e80bef0
http://hdl.handle.net/11567/970344
http://hdl.handle.net/11567/970344