Fourier Space Information Metrics for Data Acquisition
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Solution Overview
Problem
Current metrics for information processing, such as Signal-to-Noise Ratio (SNR) and cross-correlation coefficients, are inadequate for determining the amount of information collected during an experiment, especially in noisy data, and fail to integrate effectively with Shannon's information concepts, particularly in real space and Fourier space analyses.
Innovation Solution
A system and method using Fourier space information algorithms to generate new metrics like Fourier Ring Information (FRI) and Fourier Shell Information (FSI) for determining the information content in images or data sets, which includes performing Fourier transforms and evaluating transformed data sets using these algorithms to produce comparative metrics representing differences and correlated data, enabling visualization and assessment of information content and transducer efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If SNR and cross-correlation metrics are used to evaluate information content, then measurement of signal transmission fidelity is improved, but ability to determine information content in noisy data with no prior knowledge is worsened
Solution Approach 1:
The patent transforms the evaluation metric from real space to Fourier space by applying Fourier transforms to the data. This parameter change allows the system to evaluate information content across different spatial frequencies, enabling accurate measurement even when no prior knowledge of the signal exists. The Fourier space representation converts the problem from evaluating raw signal fidelity to evaluating information content distribution across frequency domains.
2Reliability
If cross-correlation coefficients are used in real space, then similarity detection is improved, but ability to detect high-frequency details is worsened due to overwhelming low-frequency components
Solution Approach 1:
The patent moves the correlation analysis from real space to Fourier space, adding a frequency dimension to the analysis. By performing Fourier transforms on the data sets and evaluating cross-correlations in the frequency domain, the system can separately analyze low-frequency and high-frequency components. This dimensional transformation allows high-frequency details to be detected without being overwhelmed by low-frequency components, as each frequency component can be evaluated independently.
3Measurement precision
If FSC/FRC metrics are used in Fourier space, then information content assessment is improved, but integration with Shannon's information concepts is worsened
Solution Approach 1:
The patent introduces an intermediary computational framework that bridges Fourier space metrics and Shannon's information concepts. The system calculates Fourier Shell Correlation or Fourier Ring Correlation coefficients, then uses these as inputs to determine information content in bits through a defined relationship. This intermediary process allows the integration of frequency-domain analysis with information theory, enabling the system to report information content in standard information-theoretic units while leveraging the advantages of Fourier space evaluation.
Data Source
AI summary
Disclosed are various examples and embodiments of systems, devices, components and methods configured to calculate the information content of data and information, which in some embodiments are based on new metrics integrating the real space and Fourier space properties of the data or information collected. Among other things, these systems, devices, components and methods provide an assessment of a full information collection chain; the information content of data in a harvesting experiment; global and local resolution; and the information content within objects of interest. Information and data metrics are measured in “bits”. The disclosed systems, devices, components and methods fall within the fields of information processing, information theory, digital signal processing, image processing, image analysis, channel capacity, signal transducers, and analogous fields, and include within their scope computing devices exploiting the new signal processing techniques and algorithms.