Tomographic Imaging Using Differential Equation Inverse Solvers
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Solution Overview
Problem
Current methods for solving electromagnetic inverse problems in biomedical imaging are limited by the need for ideal point sources, homogeneity assumptions, and the use of lossy matching media, which result in inaccurate and time-consuming image reconstruction, particularly in emergency scenarios where rapid imaging is critical.
Innovation Solution
A tomographic imaging process that involves solving electromagnetic inverse problems using partial differential equations, represented by specific differential equations and boundary conditions, to generate reconstructed images of electromagnetic properties within an object, employing scattering parameter data and a differential equation framework that does not require ideal point sources or homogeneity assumptions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Object-generated harmful factors
If lossy matching medium is used to reduce antenna mutual coupling and surface waves, then antenna coupling is reduced, but signal attenuation increases by more than 10 dB
Solution Approach 1:
The patent introduces a matching medium as an intermediary substance between the antennas and the imaged object. This matching medium serves as a mediator that reduces antenna mutual coupling and surface waves while being optimized to minimize signal attenuation, thus resolving the contradiction between reducing harmful electromagnetic interactions and preserving signal strength.
2Ease of manufacture
If conventional integral equation methods are used for image reconstruction, then the problem is solvable with approximations, but manufacturing complexity increases due to background medium selection and 2D reconstruction limitations
Solution Approach 1:
The patent changes the fundamental parameter of the mathematical approach from integral equations to differential equations. This parameter change enables 3D image reconstruction without requiring background matching media, eliminates the need for homogeneity assumptions, and removes the limitation of representing antennas as ideal point sources, thus improving manufacturing precision while maintaining ease of implementation.
3Measurement precision
If iterative forward-inverse computational procedures are used, then image reconstruction is achievable, but reconstruction time increases significantly
Solution Approach 1:
The patent inverts the conventional approach by using differential equations instead of integral equations, and by formulating the inverse problem in a way that allows direct solution methods. This inversion of the mathematical approach significantly reduces reconstruction time while maintaining or improving image accuracy, making the system suitable for emergency medical scenarios where time is critical.
4Device complexity
If 2D integral approximations are used to solve electromagnetic inverse problems, then the equations become solvable, but image accuracy decreases due to diffraction effects and approximations
Solution Approach 1:
The patent transitions from 2D integral approximations to 3D differential equations. This dimensional change allows for more accurate modeling of the electromagnetic field distribution and the imaged object without requiring simplifying approximations. The 3D differential equation approach captures diffraction effects and other electromagnetic phenomena more accurately while remaining computationally tractable through modern numerical methods.
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
This approach enables rapid and accurate reconstruction of 3D images, improving upon the limitations of existing methods by providing more precise and timely imaging results, especially in emergency medical situations.
Implementation Method 1
energizing the plurality of antennas disposed about the object to cause the antennas to radiate electromagnetic waves onto the object
Implementation Method 2
detecting the electromagnetic waves scattered by the features within the object
Data Source
AI summary
A tomographic imaging system, including a data processing component having a memory and at least one processor configured to:access scattering parameter data representing electromagnetic waves scattered by features within an object and originating from a plurality of antennas disposed around the object on a boundary S;process the scattering parameter data to generate a reconstructed image representing a spatial distribution of features within the object, said processing including:solving an electromagnetic inverse problem, wherein forward and inverse steps of the inverse problem are represented and solved as respective differential equations involving an electric field to determine values for the electric field; andprocess the determined values of the electric field to generate reconstructed image data representing one or more spatial distributions of one or more electromagnetic properties within the object.