Compressed Sensing Data Restoration with Iterative Error Verification
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Solution Overview
Problem
Current compressed sensing methods struggle to quickly and accurately determine if the original signal or image has been perfectly restored, especially in underdetermined systems, and require numerous measurements to achieve zero error.
Innovation Solution
A data restoration method using compressed sensing that involves continuously measuring data, generating data matrices from sequential measurement results, calculating errors, and iterating until a predetermined constant error is maintained, incorporating low rank matrix decomposition and sparse matrix solutions to efficiently determine perfect restoration.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of time
If compressed sensing is used to restore original signals from measured data, then the number of measurements can be reduced, but it becomes difficult to determine whether the restoration is perfect
Solution Approach 1:
The patent implements an iterative feedback mechanism where the restored signal is continuously refined through multiple measurement cycles. The system compares successive restoration results and adjusts the restoration process based on the difference between iterations, providing feedback to improve restoration accuracy while reducing the total number of measurements needed.
Solution Approach 2:
The patent employs dynamic restoration by allowing the restoration parameters and processes to adapt during the measurement and restoration cycles. The system dynamically adjusts the restoration algorithm based on the characteristics of the measured data and the convergence behavior of iterative restoration, enabling efficient restoration with fewer measurements.
2Measurement precision
If multiple measurements are performed to ensure perfect restoration, then restoration accuracy improves, but the time and complexity of the process increases
Solution Approach 1:
The patent performs preliminary actions by pre-processing the measured data and pre-establishing restoration parameters before the actual restoration process. This preliminary preparation enables faster convergence during the restoration iterations, reducing the total processing time while maintaining high restoration accuracy.
Solution Approach 2:
The patent implements a convergence-based stopping criterion that allows the restoration process to skip unnecessary iterations. By monitoring the change between successive restoration results, the system can terminate the restoration process early when the solution has converged to an acceptable level, avoiding redundant computations and improving processing speed.
3Ease of operation
If traditional compressed sensing methods are used, then restoration can be achieved, but there is no method to quickly and correctly determine that the signal has been restored
Solution Approach 1:
The patent establishes a feedback mechanism that continuously monitors restoration quality metrics and provides automatic determination of restoration completion. The system uses the difference between successive restoration results as a feedback signal to determine when restoration is complete, eliminating the need for manual verification and reducing determination time.
Solution Approach 2:
The restoration system performs self-verification by automatically determining when restoration is complete based on internal convergence criteria. The system monitors its own restoration process and autonomously determines when the signal has been successfully restored, without requiring external verification methods.
Data Source
AI summary
A data restoring method using compressed sensing and computer program product, the method includes (a) continuously measuring data for plural times to generate measurement results correspondingly, and processing the i-th measurement result using the compressed sensing, and starting to generate data matrix when times of measuring reaches a preset times of measurements N; (b) generating a first data matrix using the [(j+1)−N]th to the j—the measurements, and then generating a first restored data; (c) generating a second data matrix using the [(j+2)−N]th to the (j+1)—the measurements, and then generating a second restored data; (d) calculating an error between the first and the second restored data; (e) determining whether the error keeps constant for a predetermined number of times; (f) if not, repeating steps (c) to (e).