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Results tagged with inverse-problems
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user 9652
Inverse problems involve for example reconstruction of an object based on physical measurements and finding a best model/parameters out of a family given observed data. Typically the corresponding "forward" problems are well-posed and can be solved straightforwardly, while the inverse problems are often ill-posed. Not to be confused with the (inverse) tag.
1
vote
Accepted
Fredholm integral with functions constrained to [0;1]
There is not enough information for a thorough answer. An a priori bound on the solution may indeed help theoretically and practically. As usual with measured data you may not want to solve the equati …
- 12.7k
4
votes
Accepted
Reference Request - Recovering a function from its definite integrals (inverse problem)
Here is how you make an inverse problem of this problem: Choose a space $X$ for the function $f$ you are looking for (e.g. $L^2(0,1)$ to work in Hilbert spaces, but other spaces may be more suitable, …
- 12.7k
6
votes
Accepted
Choosing the order of Tikhonov regularization of an inverse problem
To start with: What you call Tikhonov regularization, is usually called Lavrentiev regularization (in the case of self-adjoint, non-negative definite $M$). The idea there is to shift the spectrum of $ …
- 12.7k
4
votes
Accepted
Interpretation of the integral "with respect to a plane wave" in terms of Radon transform
Sure you can't - but somehow you can. Obviously, $x\mapsto h(\theta\cdot x)$ is not an integrable function (if not $\equiv 0$) since it is constant along lines perpendicular to $\theta$. However, if $ …
- 12.7k