Tomographic Imaging with Incremental Frequency Inversion
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Solution Overview
Problem
Existing tomographic imaging methods face challenges in reconstructing the internal structure of objects due to multiple scattering of electromagnetic or acoustic waves, leading to artifacts and ill-posed inverse scattering problems, particularly in reflection mode where limited access results in insufficient spatial frequency information.
Innovation Solution
The incremental frequency inversion method reconstructs the internal structure by incrementally adding frequencies, utilizing low-frequency measurements to initialize and guide the optimization towards a global minimizer, minimizing a cost function that accounts for the difference between measured and synthesized wavefields.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If multiple scattering effects are accounted for in the inverse scattering problem, then measurement precision is improved, but device complexity increases due to non-linear optimization requirements
Solution Approach 1:
The patent segments the inverse scattering problem into a forward scattering model and an optimization inversion process. By formulating the forward model using volume integral equations with T-matrix methods, the complex multiple scattering problem is divided into manageable computational components that can be solved systematically through iterative optimization.
Solution Approach 2:
The patent transforms the inverse scattering problem by changing parameters from direct field measurements to cost function minimization. The optimization process adjusts material property parameters (permittivity, permeability) to minimize the difference between measured and calculated scattered fields, converting a difficult inverse problem into a parameter optimization task.
2Ease of operation
If reflection mode is used for imaging, then ease of operation is improved by accessing only one side, but measurement precision deteriorates due to insufficient spatial frequency information
Solution Approach 1:
The patent introduces a cost function as an intermediary between the measured scattered field data and the reconstructed image. This cost function quantifies the mismatch between measured and calculated fields, enabling the optimization process to recover spatial frequency information that would otherwise be insufficient in reflection mode imaging.
Solution Approach 2:
The patent employs a composite approach combining volume integral equation methods with T-matrix techniques to handle multiple scattering effects. This composite methodology enables accurate reconstruction from reflection mode data by properly accounting for complex wave interactions that contain embedded spatial frequency information.
3Productivity
If full bandwidth signals are used, then productivity is improved by reducing measurement time, but measurement precision worsens due to non-linear multiple scattering effects across different frequencies
Solution Approach 1:
The patent performs preliminary formulation of the forward scattering model using frequency-domain volume integral equations before conducting the inversion. By establishing the theoretical framework and cost function in advance, the system can efficiently process full bandwidth signals through systematic optimization without ad-hoc adjustments during reconstruction.
Solution Approach 2:
The patent replaces time-domain step-by-step reconstruction with a frequency-domain optimization approach. By substituting iterative time-marching methods with frequency-domain cost function minimization, the system achieves faster convergence and higher precision when processing broadband signals, overcoming the limitations of traditional sequential reconstruction 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 allows for accurate and practical reconstruction of the internal structure without requiring prior information, overcoming the challenges of non-linearity and local minima in the inverse scattering problem, achieving high resolution and accuracy.
Implementation Method 1
the received reflections often resulted from the multiple reflections and/or refractions of the propagating pulse due to multiple scattering from the structures in the material
Implementation Method 2
the received reflections often resulted from the multiple reflections and/or refractions of the propagating pulse
Implementation Method 3
a transmitter emits a signal such as an electromagnetic (EM), light or acoustic pulse, which propagates through the material
Data Source
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AI summary
A tomographic imaging system receives measurements at a set of frequencies of a wavefield scattered by an internal structure of an object, recursively reconstructs an image of the internal structure of the object until a termination condition is met, and renders the reconstructed image. For a current iteration, the system adds a frequency to a previous set of frequencies used during a previous iteration to produce a current set of frequencies, such that the added frequency is higher than any frequency in the previous set of frequencies, and reconstructs a current image of the internal structure of the object that minimizes a difference between a portion of the scattered wavefield measured at the current set of frequencies and a wavefield synthetized from the current image. A previous image determined during the previous iteration initializes the reconstruction of the current image.