Puzzle in inverse problems: Tsallis noise and Tsallis norm

Adson Alexandre Quirino da Silveira, Renato Ferreira Souza, Jonathas da Silva Maciel, Jessica Lia Santos da Costa, Daniel Teixeira dos Santos, João Medeiros Araujo, Sérgio Luiz E. F. da Silva and Gilberto Corso ()
Additional contact information
Adson Alexandre Quirino da Silveira: Universidade Federal do Rio Grande do Norte
Renato Ferreira Souza: Universidade Federal do Rio Grande do Norte
Jonathas da Silva Maciel: Senai Cimatec
Jessica Lia Santos da Costa: Universidade Federal de Minas Gerais
Daniel Teixeira dos Santos: Universidade Federal do Rio Grande do Norte
João Medeiros Araujo: Universidade Federal do Rio Grande do Norte
Sérgio Luiz E. F. da Silva: Politecnico di Torino
Gilberto Corso: Universidade Federal do Rio Grande do Norte

The European Physical Journal B: Condensed Matter and Complex Systems, 2023, vol. 96, issue 3, 1-7

Abstract: Abstract Inverse problems are challenging in several ways, and we cite the non-linearity and the presence of non-Gaussian noise. Least squared is the standard method to construct a equivalent functional for optimization, which is equivalent to the L2 norm of the misfit. Alternative norms in the optimization process are an useful strategy in the inverse problem solution. Generalized statistics can be present at two sides of the inverse problem: in the noise that pollutes the data and in the norm used in the optimization algorithm. With help of a seismic problem, we polluted the signal with a q-exponential noise (using an exponent $$q_{\text {noise}}$$ q noise ) and subsequently inverted the problem using a norm associated to a q-exponential (with an exponent $$q_{\text {inv}}$$ q inv ). The same procedure was also applied to the simpler problem of a linear fitting. We tested the hypothesis of a relation between the exponents $$q_{noise}$$ q noise and $$q_{\text {inv}}$$ q inv . The overall pattern observed is the following: inversion error are smaller for low $$q_{\text {noise}}$$ q noise and high $$q_{\text {inv}}$$ q inv . In contrast, the worst inversion is found for high polluting noise (far from Gaussian noise) and for inversion with low $$q_{\text {inv}}$$ q inv (close to the Gaussian case). Graphic abstract

Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1140/epjb/s10051-023-00496-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:eurphb:v:96:y:2023:i:3:d:10.1140_epjb_s10051-023-00496-0

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/10051

DOI: 10.1140/epjb/s10051-023-00496-0

Access Statistics for this article

The European Physical Journal B: Condensed Matter and Complex Systems is currently edited by P. Hänggi and Angel Rubio

More articles in The European Physical Journal B: Condensed Matter and Complex Systems from Springer, EDP Sciences
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().