3D Ultrasound Elasticity Data Interpolation via Sparse Matrix Optimization
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Solution Overview
Problem
Current ultrasonic imaging techniques for tissue elasticity are time-consuming and produce suboptimal results due to the need for separate steps of modeling and interpolation, which are impractical for real-time imaging, especially when dealing with noisy and sparse data.
Innovation Solution
The method formulates three-dimensional interpolation and noise reduction as a smoothness-constrained trilinear interpolation problem, using a sparse matrix to provide a simple closed-form solution that allows simultaneous interpolation and noise reduction, with error minimization and gradient constraints to balance fidelity and smoothness.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If separate steps of modeling and interpolation are used to process ultrasound data, then measurement precision is improved, but processing time increases significantly making real-time imaging impractical
Solution Approach 1:
The patent combines the separate modeling and interpolation steps into a single integrated operation. By formulating the problem as smoothness-constrained trilinear interpolation that simultaneously performs both functions, the method achieves accurate voxel data determination without the time penalty of sequential processing, enabling real-time elastography imaging.
Solution Approach 2:
The patent changes the mathematical formulation parameters by introducing smoothness constraints directly into the interpolation process. This parameter modification allows the system to achieve both high fidelity and computational efficiency by solving a constrained optimization problem that balances interpolation accuracy with processing speed through the use of sparse matrices.
2Measurement precision
If global optimization techniques such as linear programming are used to minimize error across all interpolation grid points, then measurement precision is improved, but device complexity and processing time increase making real-time imaging impractical
Solution Approach 1:
The patent applies local quality by formulating the optimization problem to consider only locally adjacent spatial data points rather than globally optimizing all grid points. This local approach uses smoothness constraints that operate on neighboring voxels, reducing computational complexity while maintaining sufficient accuracy for clinical elastography applications.
Solution Approach 2:
The patent segments the large-scale optimization problem into smaller, manageable components by using local smoothness constraints that operate on small neighborhoods of voxels. This segmentation transforms a computationally intensive global optimization problem into multiple smaller local problems that can be solved efficiently using sparse matrix techniques.
3Measurement precision
If more spatial data points are collected to improve interpolation fidelity, then measurement precision is improved, but the data becomes sparser and noisier when fewer points are available
Solution Approach 1:
The patent changes the problem formulation by introducing smoothness constraints as additional parameters in the optimization function. This allows the system to reliably determine voxel data even with sparse input points by enforcing physical plausibility through gradient constraints, effectively denoising the data while maintaining interpolation fidelity.
Solution Approach 2:
The patent introduces smoothness constraints as an intermediary mechanism that mediates between sparse spatial data points and the desired voxel values. These constraints act as a bridge that provides additional information to fill gaps in sparse data, reducing noise and improving reliability without requiring more measurement points.
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 reliable processing of ultrasound data, improving interpolation fidelity and smoothness, and is suitable for real-time imaging by using a sparse matrix that can be readily inverted, even with fewer data points than voxels, and is applicable to standard elastography ultrasound acquisitions.
Implementation Method 1
an ultrasonic probe assembly adapted to direct an ultrasound beam into tissue and receive ultrasonic echoes
Implementation Method 2
ultrasonic imaging techniques for obtaining information about tissue elasticity
Data Source
AI summary
Interpolation of ultrasound data at regular grid locations is provided by simultaneously optimizing interpolated data according to fidelity of interpolation of the voxel data to actual measured spatial data and according to a gradient of the interpolated data. This process is made amenable to real-time processing by limiting the range of interpolation to produce a sparse interpolated matrix that may be readily inverted. Artifacts and inefficiencies from successive stages of interpolation and data smoothing are thereby avoided.