Hermite Polynomial Echo Discrimination in Pulse-Echo Imaging
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current pulse-echo systems, such as sonar and ultrasound, primarily generate greyscale images and struggle to effectively discriminate and identify echoes based on additional characteristics beyond reflection, necessitating improved methods for scattering and reflection identification.
Innovation Solution
The use of Hermite polynomials to compare and classify echoes, where each polynomial is associated with a color, allowing for the generation of images that incorporate color based on the comparison, enabling the differentiation of echoes and providing additional characteristics through RGB color selection and statistical analysis.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If pulse-echo systems use conventional greyscale imaging methods, then the system complexity remains low, but the ability to discriminate and identify different types of echoes is insufficient
Solution Approach 1:
The patent segments the echo signal analysis by decomposing it into multiple Hermite polynomial components (h0, h1, h2, etc.). Each polynomial component represents a different characteristic of the echo (amplitude, time derivative, curvature), allowing the system to discriminate between different tissue types by analyzing these segmented features independently rather than treating the echo as a single greyscale value.
Solution Approach 2:
The patent transforms the echo signal from a single amplitude parameter (greyscale) into multiple parameters by fitting Hermite polynomials. This parameter transformation enables the system to extract additional characteristics (time derivatives, curvature) from the same signal, improving echo discrimination without requiring additional hardware channels.
2Loss of information
If pulse-echo systems generate only greyscale images, then the processing and display requirements remain simple, but additional characteristics such as frequency content and impedance variations cannot be visualized
Solution Approach 1:
The patent adds a new dimension to the image data by mapping Hermite polynomial coefficients to color channels (RGB). Instead of displaying only amplitude information in greyscale, the system encodes additional characteristics (time derivative from h1, curvature from h2) into color dimensions, allowing multiple echo characteristics to be visualized simultaneously in a single image without increasing processing complexity significantly.
Solution Approach 2:
The patent uses Hermite polynomial coefficients as intermediary variables that bridge the raw echo signal and the final visual representation. These coefficients serve as intermediaries that capture different aspects of the echo (amplitude, slope, curvature) and can be mapped to various display parameters (greyscale, color, texture), providing flexibility in information presentation without direct complex processing of the raw signal.
3Measurement precision
If pulse-echo systems use conventional echo reception methods, then the hardware requirements remain simple, but the ability to identify scattering versus reflection characteristics is limited
Solution Approach 1:
The patent replaces complex hardware-based discrimination methods with mathematical signal processing. Instead of using multiple physical receivers or complex antenna configurations to distinguish scattering from reflection, the system uses Hermite polynomial fitting to mathematically extract characteristic features (time derivatives, curvature) that differentiate scattering and reflection patterns, achieving the same discrimination goal through software-based signal analysis.
Data Source
AI summary
A method of forming an image of a region of interest using a pulse-echo imaging device is described. The method includes the steps of transmitting a pulse, discriminating an echo of the pulse by comparison to a plurality of Hermite polynomials, and determining a color for display based on the comparison. A system for forming an image of a region of interest is also described. The system includes a pulse-echo imaging device for transmitting a pulse and a control unit in communication with the pulse-echo imaging device. The control unit is configured to discriminate an echo of the pulse by comparison to a plurality of Hermite polynomials and determine a color for display based on the comparison.