Questions tagged [inverse-problem]
For questions pertaining to methods to estimate input parameters based upon output data.
13
questions with no upvoted or accepted answers
6
votes
0
answers
310
views
Linear vs Non Linear inverse problems: Does non-linearity help?
This is not a typical question with a deterministic answer. If this is not the right place, feel free to close it.
For the past one year I have been working on various kinds of inverse problem. Most ...
- 531
5
votes
0
answers
193
views
Inverse problem with uncertain forward operator
Suppose I want to solve a linear inverse problem. In this example we take a convolution with the kernel:
$$\frac{1}{(y^2+z^2)^{3/2}}$$
We only take a fixed $z$ for the computation and convolve with ...
- 715
5
votes
0
answers
117
views
Inverse problems with a discrete set of known parameters
What are the techniques on inverse problems to discover the distribution of parameters from a discrete set of values? For instance, I know that my domain where the PDE is defined is made up of ...
- 601
4
votes
0
answers
89
views
Identifying an unknown P.D.E. from solution data
I have a black-box simulation that produces the time evolution of a probability density function p(x, t) in 1 dimension from arbitrary initial conditions p(x, 0). The underlying simulation occurs on a ...
- 41
3
votes
0
answers
129
views
Invert a huge sparse operator;
please help me with this question, I want to invert a huge sparse (non-circulant) this below in a $Ax=y$ equation:
$$(\lambda I+ \beta D+ \sigma C)x=y$$
where
I is an Identity Matrix,D is a Diagonal ...
- 31
3
votes
0
answers
121
views
Creating FEM mesh for image region — what is the most suitable shape function?
I wish to create a FEM mesh to solve an inverse elasticity problem, for an irregular domain. This domain is given by a medical image, so it is discretised and each square on the grid has one scalar ...
- 209
2
votes
0
answers
35
views
adjoint method for degenerate problems
For the sake of the rest of the question, I'm interested in the porous medium equation
$$S\frac{\partial\phi}{\partial t} = \nabla\cdot K\phi\,\nabla\phi$$
where $S$ and $K$ are spatially-variable ...
- 9,168
2
votes
0
answers
53
views
SPECT reconstrction using MLEM
In Single-Photon Emission Computerized Tomography (SPECT) parallel beam reconstruction using Maximum-Likelihood Expectation–Maximization(MLEM), is it sufficient to scan the object around 180 degree? ...
2
votes
0
answers
55
views
Inverted value is not consistent with expectation
We have a group of observations
$$y = f(x_1, x_2, x_3) \enspace .$$
We have also a forward model $y = f(x_1, x_2)$. The forward model does not include $x_3$ because $x_3$ might include dozens of ...
- 21
2
votes
0
answers
167
views
Inverse problem with a rank-1 update
I hope you can help me out with this. I have to find the solution x to an inverse system
$$
x=A^{-1}b
$$
This inverse problem is basically a least square problem with a rank-1 update.
$$
x=[uv^{T}...
- 21
1
vote
0
answers
83
views
Can x-ray back-projection be converted to hard-field magnetic induction tomography?
This is a question about hard-field back-projection as used in x-ray tomography, applied magnetic induction tomography. Al-Zeibak and Saunders have shown that x-ray filtered backprojection can be ...
1
vote
0
answers
188
views
Simple MCMC Algorithm in Matlab
I would be really glad to get some specific advise on how to implement a simple MCMC algorithm (in Matlab, if possible). I'm not yet too familiar with optimization methods. My problem goes as follows:
...
- 11
1
vote
0
answers
438
views
How can I efficiently solve $Ax$=$b$ given $A$ is symmetric and contains very small (even negative) eigenvalues using EIGEN
Currently I am using the EIGEN C++ library to try to solve $x$ from the equation $Ax$ = $b$. One problem I encountered is that the matrix $A$ is a correlation matrix with size > 5000 and can ...
- 11