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Suman Kumar Sahoo

Publications and source records attributed to Suman Kumar Sahoo.

24 records · Page 2Linked to original sources
arXiv2020

Microlocal inversion of a 3-dimensional restricted transverse ray transform of symmetric $m$-tensor fields

We study the problem of inverting a restricted transverse ray transform to recover a symmetric $m$-tensor field in $\mathbb{R}^3$ using microlocal analysis techniques. More precisely, we prove that a symmetric $m$-tensor field can be recovered up to a known singular term and a smoothing term if its transverse ray transform is known along all lines intersecting a fixed smooth curve satisfying the Kirillov-Tuy condition.

math.AP↗
arXiv2020

Injectivity and range description of first $(k+1)$ integral moment transforms over $m$-tensor fields in $\mathbb{R}^n$

In this work, we prove a new decomposition result for rank $m$ symmetric tensor fields which generalizes the well known solenoidal and potential decomposition of tensor fields. This decomposition is then used to describe the kernel and to prove an injectivity result for first $(k+1)$ integral moment transforms of symmetric $m$-tensor fields in $\mathbb{R}^n$. Additionally, we also present a range characterization for first $(k+1)$ integral moment transforms in terms of the John's equation.

math.AP↗
arXiv2019

Momentum Ray Transforms, II: Range Characterization In the Schwartz space

The momentum ray transform $I^k$ integrates a rank $m$ symmetric tensor field $f$ over lines of ${\R}^n$ with the weight $t^k$: $ (I^k\!f)(x,ξ)=\int_{-\infty}^\infty t^kłf(x+tξ),ξ^m\r\,dt. $ We give the range characterization for the operator $f\mapsto(I^0\!f,I^1\!f,\dots, I^m\!f)$ on the Schwartz space of rank $m$ smooth fast decaying tensor fields. In dimensions $n\ge3$, the range is characterized by certain differential equations of order $2(m+1)$ which generalize the classical John equations. In the two-dimensional case, the range is characterized by certain integral conditions which generalize the classical Gelfand -- Helgason -- Ludwig conditions.

math.AP↗
arXiv2018

Symmetry from sectional integrals for convex domains

Let $Ω$ be a bounded convex domain in $\mathbb{R}^n$ ($n \ge 2$). In this work, we prove that if there exists an integrable function $f$ such that it's Radon transform over $(n-1)$-dimensional hyperplanes intersecting the domain $Ω$ is a strictly positive function of distance to the nearest parallel supporting hyperplane to $Ω$, then $Ω$ is a ball and the function $f$ is a unique radial function about the centre of $Ω$.

math.CA↗
arXiv2018

Momentum ray transforms

The momentum ray transform $I^k$ integrates a rank $m$ symmetric tensor field $f$ over lines with the weight $t^k$: $ (I^k\!f)(x,ξ)=\int_{-\infty}^\infty t^k\langle f(x+tξ),ξ^m\rangle\,dt. $ In particular, the ray transform $I=I^0$ was studied by several authors since it had many tomographic applications. We present an algorithm for recovering $f$ from the data $(I^0\!f,I^1\!f,\dots, I^m\!f)$. In the cases of $m=1$ and $m=2$, we derive the Reshetnyak formula that expresses $\|f\|_{H^s_t({\mathbb{R}}^n)}$ through some norm of $(I^0\!f,I^1\!f,\dots, I^m\!f)$. The $H^{s}_{t}$-norm is a modification of the Sobolev norm weighted differently at high and low frequencies. Using the Reshetnyak formula, we obtain a stability estimate.

math.AP↗