An Introduction to the Mathematical Theory of Inverse Problems

Abstract.We review important ideas on nuclear and quark matter description on the basis of hightemperature field theory concepts, like resummation, dimensional reduction, interaction scale separation and spectral function modification in media. Statistical and thermodynamical concepts are spotted in the light of these methods concentrating on the -partially still open-problems of the hadronization process.

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“…(52) leads to close results for w(m) from close functions for σ(T ). In fact this is known as the "inverse imaging problem" [123][124][125].…”

Section: Continuous Mass Fits To Lattice Eosmentioning

confidence: 99%

Nuclear and quark matter at high temperature

2017

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“…Equation (12) is always solvable and has a minimal 2-norm solution + , which is equal to † , where † is the Moore-Penrose inverse of [14]. If (1) is inconsistent, which is only caused by the noise, can be decomposed into two parts 0 + , where 0 ∈ R( ), ∈ R( ) ⊥ , and is caused by noise.…”

Section: Preparationsmentioning

confidence: 99%

Weighting Algorithm and Relaxation Strategies of the Landweber Method for Image Reconstruction

Han

Wang

2018

Mathematical Problems in Engineering

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The iterative approach is important for image reconstruction with ill-posed problem, especially for limited angle reconstruction. Most of iterative algorithms can be written in the general Landweber scheme. In this context, appropriate relaxation strategies and appropriately chosen weights are critical to yield reconstructed images of high quality. In this paper, based on reducing the condition number of matrix 푇 , we find one method of weighting matrices for the general Landweber method to improve the reconstructed results. For high resolution images, the approximate iterative matrix is derived. And the new weighting matrices and corresponding relaxation strategies are proposed for the general Landweber method with large dimensional number. Numerical simulations show that the proposed weighting methods are effective in improving the quality of reconstructed image for both complete projection data and limited angle projection data.

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“…It is easy to verify that minimizing (27) can be reduced to solve the normal equation (see Kirsch, 1996, e.g. )…”

Section: For Any Givenāmentioning

confidence: 99%

Simultaneous Inversion for Space-Dependent Diffusion Coefficient and Source Magnitude in the Time Fractional Diffusion Equation

Zhang¹,

Li²,

Jia³

et al. 2013

JMR

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We deal with an inverse problem of simultaneously identifying the space-dependent diffusion coefficient and the source magnitude in the time fractional diffusion equation from viewpoint of numerics. Such simultaneous inversion problem is often of severe ill-posedness as compared with that of determining a single coefficient function. The forward problem is solved by employing an implicit finite difference scheme, and the inverse problem is solved by applying the homotopy regularization algorithm with Sigmoid-type homotopy parameter. The inversion solutions approximate to the exact solutions demonstrating that the proposed algorithm is efficient for simultaneous inversion problems in the fractional diffusion equation.

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An Introduction to the Mathematical Theory of Inverse Problems

Cited by 1,042 publications

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Nuclear and quark matter at high temperature

Nuclear and quark matter at high temperature

Weighting Algorithm and Relaxation Strategies of the Landweber Method for Image Reconstruction

Simultaneous Inversion for Space-Dependent Diffusion Coefficient and Source Magnitude in the Time Fractional Diffusion Equation

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