Tensor Signal Detection Using Trace Invariants Without Matrix Reduction
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Solution Overview
Problem
Existing signal detection methods for multi-channel images and hyper-spectral data represented as tensors of order greater than or equal to 3 suffer from performance loss due to data reduction into matrices, leading to noise corruption.
Innovation Solution
A method involving the computation of an invariance value based on trace invariants for tensors, using a linear combination of melonic, tadpole, tetrahedral, and pillow-type invariants, and comparing this value with reference values to estimate the signal-to-noise ratio, delivering the tensor for processing only if the ratio is non-zero.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If data reduction is applied to convert tensors into matrices or vectors, then signal detection methods can be applied, but performance loss occurs in signal detection
Solution Approach 1:
The patent extends signal detection from matrix dimension (2D) to tensor dimension (3D or higher) by defining trace invariants specifically for tensors. This allows direct application of signal detection methods on tensor-ordered data without reduction, preserving the inherent multi-way structure and improving detection performance while maintaining method applicability through generalized mathematical formulations.
2Adaptability or versatility
If tensors are converted to matrices for processing, then existing processing methods can be used, but noise corruption increases
Solution Approach 1:
The patent extracts and utilizes the essential trace invariant property from matrix theory and extends it to tensors by defining appropriate tensor contractions. This extraction of the core mathematical concept (trace invariance) allows the development of tensor-specific signal detection methods that operate directly on tensor data, avoiding the noise-introducing conversion to matrices while maintaining compatibility with the underlying mathematical principles.
3Measurement precision
If trace invariants are computed for tensors, then signal detection accuracy improves, but computational complexity increases
Solution Approach 1:
The patent segments the computation of tensor trace invariants into distinct contraction operations on tensor modes. By breaking down the invariant computation into sequential mode contractions rather than treating it as a monolithic operation, the method reduces computational complexity while maintaining accuracy. This segmentation allows for optimized implementation and potential parallelization of individual contraction steps.
Data Source
AI summary
The present description concerns a method of detecting a useful signal, the method comprising the acquisition of a raw signal, by a sensor; the delivery of the raw signal, to a processing device, the signal being represented by a tensor of order d greater than or equal to 3; the computing of an invariance value associated with the tensor, the invariance value being computed based on at least one trace invariant for tensors of order d; the comparison of the invariance value associated with the tensor with a first reference value; based on the comparison, the provision, by the processing device, of an estimate of the signal-to-noise ratio of the raw signal; and if the estimated signal-to-noise ratio is different from 0, the provision of the tensor to a circuit configured to process the raw signal.