Compressed Sensing Signal Reconstruction With Reduced Correlation Computation
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Solution Overview
Problem
The complexity of calculating correlations between residual errors and columns in the sensing matrix during signal reconstruction in compressed sensing technologies leads to high computational complexity, hindering efficient signal recovery.
Innovation Solution
The proposed method reduces computational complexity by determining correlations between residual errors and multiple columns in the sensing matrix by subtracting products of base differences and difference coefficients, allowing for efficient signal reconstruction while ensuring proper recovery.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If the orthogonal matching pursuit method is used to determine each column of the base matrix by calculating correlation between residual error and columns in the sensing matrix, then the signal can be properly reconstructed, but the computational complexity becomes extremely high
Solution Approach 1:
The patent pre-calculates and stores the correlation matrix T^H T before the actual signal reconstruction process. This preliminary action allows the iterative algorithm to reuse pre-computed values instead of recalculating correlations between residual errors and sensing matrix columns at each iteration, significantly reducing computational complexity while maintaining reconstruction accuracy
Solution Approach 2:
The patent extracts and stores only the essential correlation information (the correlation matrix T^H T) from the sensing matrix T before the iterative process. By separating the pre-computable correlation structure from the iterative update process, the method eliminates redundant calculations while preserving the necessary information for accurate signal reconstruction
2Reliability
If the conventional sampling process is used to collect data for the original signal, then the data collection follows the Nyquist sampling theorem, but a majority of the collected data is discarded during compression
Solution Approach 1:
The patent changes the fundamental parameter of data collection from Nyquist sampling (collecting N samples) to compressed sensing measurement (collecting M measurements where M < N). By changing the sampling parameter from full sampling to sparse measurement, the system achieves reliable signal recovery while retaining only the essential information needed for reconstruction, thereby avoiding discarding majority of data
Data Source
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AI summary
Embodiments of the present invention provide a signal reconstruction method and apparatus. The method includes: determining a correlation between a first residual error and multiple columns in a sensing matrix according to a measured value of an original signal and the sensing matrix, and determining a first array most correlative to the measured value of the original signal in the sensing matrix according to the correlation between the first residual error and the multiple columns in the sensing matrix; determining a correlation between a kth residual error and the multiple columns in the sensing matrix according to a correlation between a (k-1)th residual error and the multiple columns in the sensing matrix, and determining a kth array most correlative to the measured value of the original signal in the sensing matrix according to the correlation between the kth residual error and the multiple columns in the sensing matrix, where 2 ≤ k ≤ K; and recovering the original signal after determining a Kth array most correlative to the measured value of the original signal in the sensing matrix. The signal reconstruction method and apparatus in the embodiments of the present invention can reduce the amount of calculation for reconstructing the signal.