Electrical Impedance Tomography With Fewer Electrodes and Unique Inversion
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Solution Overview
Problem
Traditional two-dimensional resistance tomography requires a large number of periphery contact electrodes to generate high-resolution tomographic images, leading to computational inefficiencies and low resolution due to an ill-defined mesh problem and poorly placed electrodes.
Innovation Solution
The method employs an orthogonal basis with a maximum number of elements determined by the number of electrodes, strategically placing electrodes for sensitivity and using optimized current and voltage pairs to enhance resolution and reduce computational time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a large number of periphery contact electrodes are used to generate high-resolution tomographic images, then measurement precision is improved, but device complexity and computational requirements increase significantly
Solution Approach 1:
The patent transforms the inverse problem from a mesh-based approach to a polynomial basis approach by changing the mathematical parameters. Instead of using complex mesh algorithms with many electrodes, the invention uses orthogonal polynomial basis functions where the number of parameters is determined by the maximum polynomial degree, not the number of electrodes. This parameter transformation allows achieving the same or better resolution with fewer electrodes.
Solution Approach 2:
The patent extracts only the essential measurement information needed for tomographic imaging by using polynomial basis functions that capture the dominant features of the resistance distribution. Rather than processing all possible electrode combinations through complex mesh algorithms, the invention extracts the critical parameters represented by polynomial coefficients, reducing computational complexity while maintaining imaging quality.
2Productivity
If traditional mesh algorithms are used with limited electrode data, then computational resources are reduced, but measurement precision and solution uniqueness deteriorate
Solution Approach 1:
The patent changes the mathematical formulation from solving a mesh-based inverse problem to fitting orthogonal polynomial basis functions. The number of polynomial parameters is explicitly controlled by the maximum degree parameter, creating a well-posed problem where the number of parameters matches the available measurements. This ensures a unique solution while maintaining computational efficiency, as polynomial fitting is inherently more stable and faster than mesh-based iterative algorithms.
Solution Approach 2:
Instead of using measurements to infer mesh properties through complex iterative algorithms, the patent inverts the approach by directly fitting polynomial basis functions to the measurements. This inversion simplifies the computational problem from an ill-posed inverse problem to a well-posed parameter estimation problem, ensuring uniqueness and stability without requiring excessive computational resources.
3Device complexity
If electrodes are poorly placed or measurement pairs are non-optimal, then device complexity is reduced, but measurement precision and signal-to-noise ratio deteriorate
Solution Approach 1:
The patent changes the optimization criterion from electrode placement geometry to polynomial degree selection. Rather than spending complexity on optimizing electrode positions and measurement pairs, the invention controls the information content through the polynomial degree parameter. This parameter change simplifies the design process while ensuring optimal use of available measurements through the mathematical properties of orthogonal polynomials.
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 achieves high-resolution tomographic imaging by ensuring a unique solution and reducing computational waste, while improving signal-to-noise ratio and robustness against noise.
Implementation Method 1
Two-dimensional resistance tomography utilizes a resistive elastomer sensing membrane to produce a change in resistance when contact pressure is applied
Implementation Method 2
Resistance change is measured through periphery contact electrodes to generate a tomographic image
Data Source
AI summary
The disclosed 2-D resistance tomographic imaging method optimizes computation speed for performing electrical impedance tomography using a model-space with a minimal number of orthonormal polynomial basis functions to describe discernable features in the 2-D resistance tomographic image, determining a minimal number of contacts to take fewer measurements than available information based on the number of basis functions, selecting a subset of rows of a matrix of calculated sensitivity coefficients to form a square Jacobian matrix for a linearized forward problem to be solved and inversion of the linear forward problem, and solving an inverse problem based on the square Jacobian matrix by performing at least one iteration of a Newton's method solve.