Tensor Signal Detection Using Trace Invariants Without Data Reduction
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Solution Overview
Problem
Existing signal detection methods for multi-channel images and hyperspectral data represented as tensors of order greater than or equal to 3 suffer from performance loss due to data reduction to matrices, leading to ineffective noise handling.
Innovation Solution
A method involving a sensor that acquires raw signals as tensors, calculates an invariance value based on trace invariants, compares it with reference values, and processes the signal if the signal-to-noise ratio is non-zero, without converting tensors to matrices.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If data reduction is applied to convert tensors to matrices or vectors, then signal detection methods can be applied, but performance is lost
Solution Approach 1:
The patent changes the mathematical parameters by using trace invariants of tensors directly, rather than converting to matrices. This allows signal detection methods to operate on tensor data in its native form, preserving the full data structure and avoiding performance loss associated with data reduction.
Solution Approach 2:
The patent replaces the mechanical process of data reduction (converting tensors to matrices/vectors) with a direct mathematical approach using trace invariants. This substitution eliminates the need for dimensionality reduction while maintaining compatibility with existing signal detection algorithms.
2Ease of operation
If tensors are converted to matrices or vectors, then existing signal detection methods can process the data, but noise handling becomes ineffective
Solution Approach 1:
The patent changes the representation parameter from matrix/vector form to tensor form with trace invariants. This allows existing signal detection methods to operate directly on tensor data without conversion, maintaining both ease of operation and effective noise handling capabilities.
Solution Approach 2:
The patent creates a universal approach where trace invariants enable signal detection methods to handle tensor data directly, making the system multi-functional without requiring separate processing paths for different data types. This maintains compatibility with existing methods while improving noise handling.
3Productivity
If data reduction is performed to apply signal detection methods, then processing can be performed, but data integrity is compromised
Solution Approach 1:
The patent substitutes the data reduction mechanism with a direct tensor-based approach using trace invariants. This replacement maintains data integrity by avoiding the information loss inherent in converting tensors to matrices or vectors, while still enabling processing through established signal detection methods.
Data Source
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AI summary
The present description relates to a method for detecting a useful signal, the method comprising: - acquiring a raw signal, by a sensor; - providing the raw signal, to a processing device, the signal being represented by a tensor of order d greater than or equal to 3; - calculating an invariance value associated with the tensor, the invariance value being calculated on the basis of at least one trace invariant for tensors of order d; - comparing the invariance value associated with the tensor with a first reference value; - based on the comparison, providing, by the processing device, an estimate of the signal-to-noise ratio of the raw signal; and - if the estimated signal-to-noise ratio is different from 0, providing the tensor to a circuit configured to process the raw signal.