Questions tagged [inverse-problems]
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.
11 questions
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Is $\delta(df \wedge df)=0$ an Euler-Lagrange equation?
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- 6,741
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Solving for a set of points from projections
Consider a set of $N$ points in $n$-dimensional space, i.e.
\begin{align*}
S = \{x_1, \dots, x_N\} \subset \mathbb R^n.
\end{align*}
Let $v \in \mathbb R^n$ and consider the image set (not counting ...
user45183
23
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1
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Geodesics in finite groups
It seems that I can generalize a result from compact, connected Lie groups to finite groups, but in order to do so, I need to have some kind of geodesics on finite groups.
Below is a proposition for ...
- 8,086
17
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1
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An explicit reconstruction of a matrix from its minors
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Let $V$ be a $d$-dimensional real vector space. ($d \ge 4$). Fix an odd integer $...
- 6,741
8
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1
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Inverting a function
I posted this question on crypto.SE but got no answer:
Let $w = a_0 \cdot a_1 \cdots a_{n-1} $ be a word from $ \{0,1\}^n $, $|w| = n$
Let $m = \sum_{i=0}^{n-1}{ a_i \cdot 2 ^ {n-1-i} } $ be the ...
user6671
5
votes
2
answers
204
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Reconstructing set of points from one-dimensional images
Consider a set of $N$ points in $n$-dimensional space, i.e.
\begin{align*}
\{x_1, \dots, x_N\} \subset \mathbb R^n.
\end{align*}
Let us be given a finite family of non-injective matrices
\begin{...
user45183
4
votes
1
answer
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Invertibility of an inverse problem
Let $p$ be a scalar field $p: \mathbb R^n \to \mathbb R$. I encountered the problem of reconstructing an unknown density $p$ from its integral values
$$I(t,z) = \int_{V_t} p(x) dS$$
along a one-...
user45183
3
votes
2
answers
947
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Can one hear the shape of a drum for operators?
M. Kac in his famous paper "Can one hear the shape of a drum?" asked whether one can "hear" the area of the ambient domain by looking at the spectral picture. Although he was not the first who came up ...
- 1,583
2
votes
1
answer
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Non-Fourier complete orthogonal basis?
The Fourier Transform (FT)
Is orthogonal: inner product of one basis, $e^{j\omega_0}$, with any other basis, $e^{j\omega_1}$, is zero
Is invertible: info-preserving, has inverse function
Is energy-...
1
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2
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Certain inverse problem related to moments
Suppose $D\subset \mathbb C$ is a smoothly bounded domain and it contains the origin. Let $ds$ denote the arc length measure on $\partial D.$ I am interested in the following two inverse problems (...
- 1,583
0
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0
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Alternative to the Sampling Theorem / Invertible transform with sampling criteria
I seek a transform $T$ that operates on real-valued $x(t)$, that
Is perfectly invertible
Has discrete counterpart with continuous reconstructor
Provides conditional reconstruction guarantees
...