Fourier Sparse Reconstruction for Large Sensor Set Compression
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Solution Overview
Problem
Current compressed sensing techniques fail to effectively manage large sets of signals or data from multiple sensors distributed in a geographical area, leading to an exponential increase in possible output values, which exceeds the capabilities of current data storage and computation technologies.
Innovation Solution
The method involves compressing original signals in the Fourier frequency domain by truncating insignificant Fourier bases and estimating Fourier coefficients, allowing for reconstruction of original signals using a sparse regression technique and a Fourier basis set, with a threshold value determining the trade-off between accuracy and computational efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If compressed sensing is applied to set functions with multiple input sets from distributed sensors, then signal compression and reconstruction capability is improved, but the total number of possible output values increases exponentially making data storage and computation infeasible
Solution Approach 1:
The patent extracts only the essential Fourier coefficients that significantly contribute to signal reconstruction, discarding insignificant coefficients below a threshold. This extraction approach reduces the data volume from exponential (2^N possible output values) to a manageable subset of critical coefficients, enabling storage and processing while maintaining reconstruction quality.
Solution Approach 2:
The patent transforms the signal representation from the original domain to the Fourier frequency domain, changing the parameter space. By operating in the frequency domain and applying thresholding to Fourier coefficients, the system converts an intractable exponential-scale problem into a manageable sparse coefficient representation, fundamentally changing how the data is stored and processed.
2Measurement precision
If all Fourier bases are retained for accurate signal reconstruction, then reconstruction accuracy is improved, but computational complexity and data storage requirements increase significantly
Solution Approach 1:
The patent applies partial action by retaining only the most significant Fourier coefficients above a threshold value, rather than processing all possible coefficients. This selective approach achieves sufficient reconstruction accuracy for practical applications while dramatically reducing computational complexity and storage requirements, accepting that not all coefficients are equally important.
Solution Approach 2:
The patent applies different treatment to different Fourier coefficients based on their significance. Significant coefficients (above threshold) are retained with high precision for accurate reconstruction, while insignificant coefficients (below threshold) are discarded. This local differentiation optimizes the balance between accuracy and complexity by allocating computational resources only where needed.
Data Source
AI summary
The present invention relates to a compressed sensing apparatus for compressed sensing of a set function consisting of a plurality of input sets containing a group of data. The apparatus includes: a plurality of sensing units acquiring a group of sampling data representing a plurality of sampling sets selected out of the plurality of input sets; a compression and computation unit enabling a compression to the group of data based on the group of sampling data in accordance with a Fourier basis set generated on the basis of the plurality of input sets and sampling sets, and a computation to compute a Fourier coefficient set based on a sparse regression technique which is in relation with the Fourier basis set; and a reconstruction unit predicting the group of data based on the Fourier coefficient set.