Rohit Kumar Mishra

activity

20172026

most citedSupport Theorems and an Injectivity Result for Integral Moments of a Symmetric m-Tensor Field

27 citations · 50 across the 26 of their papers we have counts for

collaborators

26 papers

math.CA2026

Gaussian beam Radon transform for tensor fields in $R^{2}$

Rohit Kumar Mishra, Souvik Roy, Indrani Zamindar

In this article, we introduce and study a set of generalized Gaussian beam Radon transforms (GbRt) acting on tensor fields in $R^{2}$ . The operators considered include longi…

math.AP2026

An Inverse problem for a fourth order nonlinear Schrödinger equation (NLS)

Rohit Kumar Mishra, Anamika Purohit, Suman Kumar Sahoo

We study an inverse problem for the time-dependent nonlinear fourth-order Schrödinger equation on both compact Euclidean domains and compact Riemannian manifolds, (say) $M$ . This m…

math.CA2025

The head-wave transform

Maarten V. de Hoop, Antti Kykkänen, Rohit Kumar Mishra

We introduce and study a new integral ray transform called the head-wave transform. The head-wave transform integrates a function along a piecewise linear (in general geodesic) pat…

math.CA2025

Reconstruction of scalar functions and vector fields from weighted V-line transforms with swinging branches

Gaik Ambartsoumian, Rohit Kumar Mishra, Indrani Zamindar

Weighted V-line transforms map a symmetric tensor field of order $m \geq 0$ to a linear combination of certain integrals of those fields along two rays emanating from the same vertex.…

math.AP2025

Inversion of generalized Radon transform over symmetric $m$ -tensor fields in $R^{n}$

Anuj Abhishek, Rohit Kumar Mishra, Chandni Thakkar

In this work, we study a set of generalized Radon transforms over symmetric $m$ -tensor fields in $R^{n}$ . The longitudinal/transversal Radon transform and corresponding weig…

math.NA2024

Tensor tomography using V-line transforms with vertices restricted to a circle

Rohit Kumar Mishra, Anamika Purohit, Indrani Zamindar

In this article, we study the problem of recovering symmetric $m$ -tensor fields (including vector fields) supported in a unit disk $D$ from a set of generalized V-line tra…

math.NA2024

V-line tensor tomography: numerical results

Gaik Ambartsoumian, Rohit Kumar Mishra, Indrani Zamindar

This article presents the numerical verification and validation of several inversion algorithms for V-line transforms (VLTs) acting on symmetric 2-tensor fields in the plane. The a…

math.CA2024

Inversion of generalized V-line transforms of vector fields in $R^{2}$

Rahul Bhardwaj, Rohit Kumar Mishra, Manmohan Vashisth

This article studies the inverse problem of recovering a vector field supported in $D_{R}$ , the disk of radius $R$ centered at the origin, through a set of generalized broke…

math.AP2024

Inversion formula, Unique continuation property, and range characterization of the mixed ray transform in $R^{2}$

Rohit Kumar Mishra, Suman Kumar Sahoo, Chandni Thakkar

In this article, we study various aspects of the mixed ray transform of $(k + ℓ)$ -tensor fields that are symmetric in its first $k$ and last $ℓ$ indices. As a first result, w…

math.CA2024

Inversion of a restricted transverse ray transform with sources on a curve

Rohit Kumar Mishra, Chandni Thakkar

In this paper, a restricted transverse ray transform acting on vector and symmetric $m$ -tensor fields is studied. We developed inversion algorithms using restricted transverse ray…

math.CA2023

V-line 2-tensor tomography in the plane

Gaik Ambartsoumian, Rohit Kumar Mishra, Indrani Zamindar

In this article, we introduce and study various V-line transforms (VLTs) defined on symmetric 2-tensor fields in $R^{2}$ . The operators of interest include the longitudinal,…

math.NA2023

Numerical implementation of generalized V-line transforms on 2D vector fields and their inversions

Gaik Ambartsoumian, Mohammad Javad Latifi Jebelli, Rohit Kumar Mishra

The paper discusses numerical implementations of various inversion schemes for generalized V-line transforms on vector fields introduced in [6]. It demonstrates the possibility of…

math.AP2022

Inverse problem for a time-dependent Convection-diffusion equation in admissible geometries

Rohit Kumar Mishra, Anamika Purohit, Manmohan Vashisth

We consider a partial data inverse problem for a time-dependent convection-diffusion equation on an admissible manifold. We prove that the time-dependent convection term and time-d…

math.AP2022

The generalized Saint Venant operator and integral moment transforms

Rohit Kumar Mishra, Suman Kumar Sahoo

In this article, we work with a generalized Saint Venant operator introduced by Vladimir Sharafutdinov to describe the kernel of the integral moment transforms over symmetric m-ten…

math.AP2022★ 3 cited

The $C^{\infty}$ -isomorphism property for a class of singularly-weighted X-ray transforms

Rohit Kumar Mishra, François Monard, Yuzhou Zou

We study a one-parameter family of self-adjoint normal operators for the X-ray transform on the closed Euclidean disk $D$ , obtained by considering specific singularly wei…

math.OC2020

A sparsity-based nonlinear reconstruction method for two-photon photoacoustic tomography

Madhu Gupta, Rohit Kumar Mishra, Souvik Roy

We present a new nonlinear optimization approach for the sparse reconstruction of single-photon absorption and two-photon absorption coefficients in photoacoustic tomography (PAT).…

math.AP2020

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

Rohit Kumar Mishra, Suman Kumar Sahoo

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. Thi…

math.CA2020★ 11 cited

Generalized V-line transforms in 2D vector tomography

Gaik Ambartsoumian, Mohammad Javad Latifi Jebelli, Rohit Kumar Mishra

We study the inverse problem of recovering a vector field in $R^{2}$ from a set of new generalized $V$ -line transforms in three different ways. First, we introduce the longi…

math.AP2020★ 8 cited

Determining the time dependent matrix potential in a wave equation from partial boundary data

Rohit Kumar Mishra, Manmohan Vashisth

We study the inverse problem for determining the time-dependent matrix potential appearing in the wave equation. We prove the unique determination of potential from the knowledge o…

math.AP2019

Full reconstruction of a vector field from restricted Doppler and first integral moment transforms in $R^{n}$

Rohit Kumar Mishra

We show that a vector field in $R^{n}$ can be reconstructed uniquely from the knowledge of restricted Doppler and first integral moment transforms. The line complex we consi…

math.AP2019

Range characterizations and Singular Value Decomposition of the geodesic X-ray transform on disks of constant curvature

Rohit Kumar Mishra, François Monard

For a one-parameter family of simple metrics of constant curvature ( $4 κ$ for $κ \in (- 1, 1)$ ) on the unit disk $M$ , we first make explicit the Pestov-Uhlmann range characterization o…

math.AP2019★ 1 cited

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

Venkateswaran P. Krishnan, Rohit Kumar Mishra, Suman Kumar Sahoo

We study the problem of inverting a restricted transverse ray transform to recover a symmetric $m$ -tensor field in $R^{3}$ using microlocal analysis techniques. More precise…

math.OC2019

Sparse reconstruction of log-conductivity in current density impedance tomography

Madhu Gupta, Rohit Kumar Mishra, Souvik Roy

A new non-linear optimization approach is proposed for the sparse reconstruction of log-conductivities in current density impedance imaging. This framework comprises of minimizing…

math.AP2018

Microlocal analysis of a restricted ray transform on symmetric $m$ -tensor fields in $R^{n}$

Venkateswaran P. Krishnan, Rohit Kumar Mishra

We study the microlocal inversion of the ray transform on symmetric $m$ -tensor fields restricted to all lines passing through a curve in $R^{n}$ . From this incomplete data…

Gaussian beam Radon transform for tensor fields in R2

An Inverse problem for a fourth order nonlinear Schrödinger equation (NLS)

The head-wave transform

Reconstruction of scalar functions and vector fields from weighted V-line transforms with swinging branches

Inversion of generalized Radon transform over symmetric m-tensor fields in Rn

Tensor tomography using V-line transforms with vertices restricted to a circle

V-line tensor tomography: numerical results

Inversion of generalized V-line transforms of vector fields in R2

Inversion formula, Unique continuation property, and range characterization of the mixed ray transform in R2

Inversion of a restricted transverse ray transform with sources on a curve

V-line 2-tensor tomography in the plane

Numerical implementation of generalized V-line transforms on 2D vector fields and their inversions

Inverse problem for a time-dependent Convection-diffusion equation in admissible geometries

The generalized Saint Venant operator and integral moment transforms

The C∞-isomorphism property for a class of singularly-weighted X-ray transforms

A sparsity-based nonlinear reconstruction method for two-photon photoacoustic tomography

Injectivity and range description of first (k+1) integral moment transforms over m-tensor fields in Rn

Generalized V-line transforms in 2D vector tomography

Determining the time dependent matrix potential in a wave equation from partial boundary data

Full reconstruction of a vector field from restricted Doppler and first integral moment transforms in Rn

Range characterizations and Singular Value Decomposition of the geodesic X-ray transform on disks of constant curvature

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

Sparse reconstruction of log-conductivity in current density impedance tomography

Microlocal analysis of a restricted ray transform on symmetric m-tensor fields in Rn

Gaussian beam Radon transform for tensor fields in $R^{2}$

Inversion of generalized Radon transform over symmetric $m$ -tensor fields in $R^{n}$

Inversion of generalized V-line transforms of vector fields in $R^{2}$

Inversion formula, Unique continuation property, and range characterization of the mixed ray transform in $R^{2}$

The $C^{\infty}$ -isomorphism property for a class of singularly-weighted X-ray transforms

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

Full reconstruction of a vector field from restricted Doppler and first integral moment transforms in $R^{n}$

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

Microlocal analysis of a restricted ray transform on symmetric $m$ -tensor fields in $R^{n}$