# Questions tagged [inverse-problem]

For questions pertaining to methods to estimate input parameters based upon output data.

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### Numerical methods for inverting integral transforms?

I'm trying to numerically invert the following integral transform: $$F(y) = \int_{0}^{\infty} y\exp{\left[-\frac{1}{2}(y^2 + x^2)\right]} I_0\left(xy\right)f(x)\;\mathrm{d}x$$ So for a given $F(y)$ ...
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### First appearance of the phrase "inverse crime"

In research on inverse problems, it's common to construct a synthetic data set from a known set of parameters and then test whether the inversion technique can reconstruct those parameters. In doing ...
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### How can I determine the initial values of pseudo-random number generator if the sequence is given?

Suppose I knew that a random number sequence was generated by a linear congruential generator. That is, $x_{n+1}=(aX_n+c) \bmod m$ If I am given the entire period (or at least a large contiguous ...
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### Edge and Nodal finite element methods in MATLAB for Magnetic induction tomography

What is the difference between edge finite elements and nodal finite elements? This for use in modeling the eddy current problem in classical electromagnetism. I am attempting to convert MATLAB code ...
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### an over view of sparsity promoting inversion techniques [closed]

I have a function called f(x) which is convex and I can have access to its first order derivative , my objective function is $$\ J(\bf{x}) = f(\bf{x}) + \lambda |\bf{x}|_0$$ \ \bigtriangledown ...
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### Computing preconditioner for a non-linear conjugate gradient implementation

Consider the following steps for the $i$-th non-linear conjugate gradient iteration, in the context of 3D electromagnetic inversion, and as discussed in (Newman and Boggs, 2004): (1) set $i = 1$, ...