# Tagged Questions

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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 ...
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### Partial recovery from Radon transform

Let $f : \mathbb R^3 \to \mathbb R$ be an integrable function. Let $\eta$ be a one-dimensional subspace of $\mathbb R^3$. We denote $p+\eta$ the affine subspace (a line) which is obtained by ...
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### Generalized Radon transform (Relaxed sufficient condition for invertibility)

The generalized Radon transform maps a function $f \in L^1(\mathbb R^n)$, usually interpreted as a density of an object, to its integral value over an $(n-1)$-dimensional affine subspace. To be more ...
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### “Limited angle” in n-dimensional Radon transform?

The Radon transform in two-dimensions is well studied. It maps a sufficiently nice function $f: \mathbb R^2 \to \mathbb R$ to its line integral along a certain line $L$, i.e. \begin{align*} ...
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This question might have a formulation in higher dimensions, but for now let's deal with the 2 dimensional Radon transform: $\newcommand{\R}{\mathbb{R}}$ $$Rf(\varphi,s)=\int_{-\infty}^\infty ... 3answers 400 views ### Rate of growth of an explicit integral Let$$J_1=\int_0^1\frac{1}{\sqrt{1-t_2}}dt_2,J_2=\int_0^1 \int_0^{t_2}\frac{1}{\sqrt{1-t_2}}(\frac{1}{\sqrt{1-t_3}}+\frac{1}{\sqrt{t_2-t_3}})dt_3dt_2,$$J_3=\int_0^1 ... 1answer 329 views ### Inversion of Radon transform by incomplete data: specific case Let R[f](p,t) denote the Radon transform of smooth function f(x) \colon \mathbb{R}^n \to \mathbb{R} with compact support in \mathbb{R}^n_+:$$ R[f](p,t) = \int\limits_{x \cdot p = t} f(x) dx. ...
Given a family of hypersurfaces $H_{t,p} =$ {$x \in \mathbb{R}^n \mid g(x,p) = t$} one defines a generalized Radon transform $R$ of a function $u \colon \mathbb{R}^n \to \mathbb{R}$ as  R[u] ...