Object Reflectivity Tomography With Reduced Computational Domains
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Solution Overview
Problem
Generating high-resolution images of objects embedded in inhomogeneous background materials is challenging due to multiple scattering and computational complexity, leading to inaccurate reconstructions and position ambiguity in existing tomographic imaging methods.
Innovation Solution
A tomographic imaging system that incorporates wave propagation integral equations with background knowledge, uses a computational domain within the inhomogeneous background medium, and employs an incremental frequency inversion framework to reconstruct images efficiently by solving an optimization problem with cross-domain and residual measurement operators.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a large size computational domain is used for image reconstruction, then the reconstruction can cover the entire object and background, but the computational complexity increases significantly
Solution Approach 1:
The computational domain is segmented into two parts: a background domain with known inhomogeneous properties and a smaller computational domain containing the object. By separating the known background region from the unknown object region, the patent reduces the computational domain size while maintaining reconstruction accuracy. The background information is used to pre-compute Green's functions and wave propagation characteristics, eliminating the need to compute these for the entire large domain.
Solution Approach 2:
The patent performs preliminary actions by pre-computing wave propagation characteristics, Green's functions, and scattering matrices for the known background medium before the actual image reconstruction. This preliminary computation of background information allows the main reconstruction process to focus only on the object region, significantly reducing computational complexity while maintaining accuracy.
2Reliability
If multiple scattering waves are considered in inhomogeneous background medium, then the wave propagation is more accurate, but the spatial frequency information is reduced leading to inaccurate images
Solution Approach 1:
The patent introduces an intermediary approach by using the known background medium properties as a mediator to pre-compute wave propagation characteristics. The background medium serves as an intermediary that allows accurate wave propagation modeling without requiring the entire inhomogeneous region to be computed during reconstruction. This intermediary computation enables accurate spatial frequency information extraction from the object region.
3Productivity
If the array of antennas is positioned to capture scattered wavefield, then the image generation can proceed, but position ambiguity occurs reducing image accuracy
Solution Approach 1:
The patent employs feedback mechanisms through iterative optimization processes that use the known background information to correct and refine the reconstructed image. The background knowledge serves as a feedback reference that helps disambiguate antenna positions and improve the accuracy of the reconstructed object properties, resolving position ambiguity issues.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
The system reduces computational complexity and improves image reconstruction accuracy by utilizing a smaller computational domain and iterative optimization, effectively visualizing internal structures with reduced spatial frequency information.
Implementation Method 1
When the incident wavefield of the electromagnetic or acoustic waves propagates inside the object and the inhomogeneous background medium, multiple scattering waves are induced on boundaries of material inside the object as well as by the inhomogeneous background medium.
Implementation Method 2
These scattered waves contain information about a spatial distribution of the material properties that may be used for reconstructing the image of the internal structure of the object.
Data Source
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AI summary
Embodiment of the present disclosure disclose a tomographic imaging system for reconstructing an image of an internal structure of an object. An incident wavefield is transmitted into the object occupying a background domain embedding the object. The incident wavefield is scattered into multiple scattered wave field by the object. The incident and scattered wavefields are measured as a total wavefield. The total wavefield propagates through a computational domain and a residual domain in the background domain that are defined by cross-domain and residual measurement operators. The total wavefield is used for the image reconstruction. The image is reconstructed by solving an optimization problem corresponding to the computational domain. The optimization problem is solved iteratively to minimize a difference between the total wavefield and a wavefield synthesized using a measurement operator and a Green's function operator from the reconstructed image. The reconstructed image is outputted via an output interface.