Abstract This paper describes the mathematical structure of ill-posed nonlinear inverse problem low-dose dental cone-beam computed tomography (CBCT) and explains advantages a deep learning-based approach to reconstruction images over conventional regularization methods. underlying reasons why CBCT is more than standard tomography. Despite this severe ill-posedness, demand for systems rapidly gr...

Ill-posedness of GNSS-based ionospheric tomography affects the stability and accuracy inversion results. Truncated singular value decomposition (TSVD) is a common algorithm reconstruction. However, TSVD method usually has low reconstruction efficiency. To resolve above problem, truncated mapping (TMSVD) presented to improve reconstructed computational authenticate effectiveness advantages TMSVD...

In many applications, such as the heat conduction and hydrology, there is a need to recover the (possibly discontinuous) diffusion coefficient a from boundary measurements of solutions of a parabolic equation. The complete inverse problem is ill posed and nonlinear, so numerical solution is quite difficult, and we linearize the problem around constant a. We study and solve numerically the linea...

The noncharacterisitic initial value problem for the one-dimensional heat equation (the solution and its rst-order spatial derivative speciied on an interval of the time axis) is well known to be ill-posed. Nevertheless, the author has proved in 4] that nonnegative solutions of this problem depend continuously on the initial data. However, this result does not solve the problem of constructing ...

The inverse geothermal problem consist of estimating the temperature distribution below the earth’s surface using temperature and heat-flux measurements on the earth’s surface. The problem is important since temperature governs a variety of the geological processes including formation of magmas, minerals, fosil fuels and also deformation of rocks. Mathematical this problem is formulated as a Ca...

in this article, a numerical approximation to the solution of the newell-whitehead equation (nwe) and cauchy problem of ill-posed non-linear diffusion equation have been studied. the presented scheme is obtained by using the derivative of the cubic b-spline quasi-interpolation (bsqi) to approximate the spatial derivative of the dependent variable and first order forward difference to approximat...

We propose a fuzzy-based approach aiming at finding numerical solutions to some classical problems. We use the technique of F-transform to solve a second-order ordinary differential equation with boundary conditions. We reduce the problem to a system of linear equations and make experiments that demonstrate applicability of the proposed method. We estimate the order of accuracy of the proposed ...