Tomographic Approach for Parametric Estimation of Local Diffusive Sources and Application to Heat Diffusion

Jovanović, Ivana; Sbaiz, Luciano; Vetterli, Martin

doi:10.1109/icip.2007.4379977

Cited by 5 publications

(4 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example, heat always flows from a position with high temperature to a position with low temperature in a medium [46]. Such a phenomenon can be captured by a functional model, in which the measurements of weather stations are just sample data points [47]. The data samples can then be used to reconstruct the diffusion process, which capture the spatio-temporal evolution of e.g.…”

Section: B Weather Diffusion Modelmentioning

confidence: 99%

Multi-Scale Bushfire Detection From Multi-Modal Streams of Remote Sensing Data

et al. 2020

View full text Add to dashboard Cite

Section: B Weather Diffusion Modelmentioning

confidence: 99%

Multi-Scale Bushfire Detection From Multi-Modal Streams of Remote Sensing Data

et al. 2020

View full text Add to dashboard Cite

“…If we change the parameters in Eq. (22) with the ones that we use in our experiments (T o 5 2 ms, f c 5 40 kHz, and B 5 2 kHz; Jovanović et al 2006) and for the two cases of SNR, we get 2 SNR 5 30 dB ! s t ' 4.4 3 10 À8 s and SNR 5 10 dB !…”

Section: A Error Analysismentioning

confidence: 99%

“…The concept is known as compressed sensing (Donoho 2006) and has been shown to be very useful for tomographic sampling in general (Jovanović 2008). …”

Section: ) Groupmentioning

confidence: 99%

Acoustic Tomography for Scalar and Vector Fields: Theory and Application to Temperature and Wind Estimation

Jovanović

Sbaiz

Vetterli

2009

Journal of Atmospheric and Oceanic Technology

Self Cite

View full text Add to dashboard Cite

Acoustic tomography is a type of inverse problem. The idea of estimating physical quantities that influence sound propagation by measuring the parameters of propagation has proven to be successful in many practical domains, including temperature and wind estimation in the atmosphere. However, in most of the previous work in this area, the algorithms used have not been proven mathematically to provide the correct solution to the inverse problem.This paper considers the problem of reconstructing 2D temperature and wind fields by using acoustic tomography setups. Primarily, it shows that the classical time-of-flight measurements are not sufficient to reconstruct wind fields. As a solution, an additional set of measurements related solely to the parameters of sound propagation-more precisely, to the angles of departure/arrival of sound waves-is suggested. To take the full benefit of this additional information, the bent-ray model of sound propagation is introduced. In this work, it is also shown that, when a temperature and a source-free 2D wind field are observed on bounded domains, the complete reconstruction is possible using only measurements of the time of flight. Conversely, the angles of departures/arrivals are sufficient to reconstruct a temperature and a curl-free 2D wind fields on bounded domains. Further, an iterative reconstruction algorithm is proposed and possible variations to the main scheme are discussed. Finally, the performed numerical simulations confirm the theoretical results, demonstrate fast convergence, and show the advantages of the adopted bent-ray model for sound propagation over the straight-ray model.

show abstract

“…Several mathematical models can apply, such as Poisson's equation for electroencephalography (EEG) [1], the heat equation for diffusive source localization [2], or the wave equation for acoustic sources [3]. Here, we focus on boundary measurements for systems goverend by the wave equation.…”

Section: Introductionmentioning

confidence: 99%

3D reconstruction of wave-propagated point sources from boundary measurements using joint sparsity and finite rate of innovation

Dogan

Jovanović

Blu

et al. 2012

2012 9th IEEE International Symposium on Biomedical Imaging (ISBI)

Self Cite

View full text Add to dashboard Cite

Reconstruction of point sources from boundary measurements is a challenging problem in many applications. Recently, we proposed a new sensing and non-iterative reconstruction scheme for systems governed by the three-dimensional wave equation. The points sources are described by their magnitudes and positions. The core of the method relies on the principles of finite-rate-of-innovation, and allows retrieving the parameters in the continuous domain without discretization.Here we extend the method when the source configuration shows joint sparsity for different temporal frequencies; i.e., the sources have same positions for different frequencies, not necessarily the same magnitudes. We demonstrate that joint sparsity improves upon the robustness of the estimation results. In addition, we propose a modified multi-source version of Dijkstra's algorithm to recover the Z parameters. We illustrate the feasibility of our method to reconstruct multiple sources in a 3-D spherical geometry.

show abstract

Tomographic Approach for Parametric Estimation of Local Diffusive Sources and Application to Heat Diffusion

Cited by 5 publications

References 7 publications

Multi-Scale Bushfire Detection From Multi-Modal Streams of Remote Sensing Data

Multi-Scale Bushfire Detection From Multi-Modal Streams of Remote Sensing Data

Acoustic Tomography for Scalar and Vector Fields: Theory and Application to Temperature and Wind Estimation

3D reconstruction of wave-propagated point sources from boundary measurements using joint sparsity and finite rate of innovation

Contact Info

Product

Resources

About