PreprintarXiv licencearXiv
A theoretically exact filtered back-propagationformula for single-time wave inversion
Abstract
We consider single-time wave inversion, that is, recovering the initial pressure f from the wave field 𝒲T f = u(·,T) at a single time T, where u solves the wave equation with sound speed c and initial data (f,0). In two dimensions this is the main reconstruction step of full-field photoacoustic projection imaging, where each camera image is a two-dimensional wave field at a single time instant. An efficient direct method is back-propagation by the Fourier multiplier 2cos(cT|ξ|). It yields exact inversion in odd dimensions but not in two. We give its error in closed form, with bounds, and derive an exact explicit filtered back-propagation f = 2𝒲T ℳK 𝒲T f in analogy to filtered backprojection for the Radon transform.
Related
- Scalable Approximate Selected Inversion Based on Single-Level Incomplete LDLT Factorization and Spectral Corrections for Large Sparse Systems
- Data Quality Assessments: A Theoretically Structured Overview of Approaches and Methods
- SILMARILS-MV: Information-Theoretically Secure Multi-Verifier Signatures with Dealer-Free Key Issuance and Linear Aggregation for Permissioned Blockchains
- Exact Entanglement Swapping through Single-Occupancy Measurements in Gaussian Fermion States
- On hyperbolic PDEs, filtered feedback control laws, and fractal-like stability crossing curves
BibTeX
@misc{haltmeier2026theoretically,
title = {{A theoretically exact filtered back-propagationformula for single-time wave inversion}},
author = {Markus Haltmeier},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35302},
eprint = {2610.35302},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35302},
}
RIS
TY - UNPB
TI - A theoretically exact filtered back-propagationformula for single-time wave inversion
AU - Markus Haltmeier
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35302
UR - https://arxiv.org/abs/2610.35302
AB - We consider single-time wave inversion, that is, recovering the initial pressure f from the wave field 𝒲_T f = u(·,T) at a single time T, where u solves the wave equation with sound speed c and initial data (f,0). In two dimensions this is the main reconstruction step of full-field photoacoustic projection imaging, where each camera image is a two-dimensional wave field at a single time instant. An efficient direct method is back-propagation by the Fourier multiplier 2cos(cT|ξ|). It yields exact inversion in odd dimensions but not in two. We give its error in closed form, with bounds, and derive an exact explicit filtered back-propagation f = 2𝒲_T ℳ_K 𝒲_T f in analogy to filtered backprojection for the Radon transform.
ER -