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Signal recovery from autocorrelation and cross-correlation data
Timothy J Schulz1, David G Voelz
1Department of Electrical and Computer Engineering, Michigan Technological University, Houghton, Michigan 49931, USA. schulz@mtu.edu
Summary
This study introduces a new iterative technique for recovering nonnegative signals using correlation functions. The method effectively preserves signal nonnegativity and improves correlation accuracy over iterations.
Area of Science:
- Signal processing
- Image reconstruction
- Applied mathematics
Background:
- Nonnegative signal recovery is crucial in various imaging and sensing applications.
- Existing methods may struggle with preserving signal nonnegativity or achieving accurate correlation approximations.
- Autocorrelation and cross-correlation functions provide valuable information about signal properties.
Purpose of the Study:
- To develop and present a novel iterative signal recovery technique.
- To ensure the preservation of nonnegativity in estimated signals.
- To enhance the accuracy of signal correlation approximations from measured data.
Main Methods:
- A new iterative algorithm is derived for signal recovery.
- The technique utilizes measurements of autocorrelation and cross-correlation functions.
- Nonnegativity constraints are incorporated into the iterative process.
Main Results:
- The iterative technique successfully preserves the nonnegativity of recovered signals.
- A sequence of signal estimates is generated, with correlations progressively improving.
- The method demonstrates effective performance on simulated active imaging data.
Conclusions:
- The developed iterative technique offers a robust approach for nonnegative signal recovery.
- The method shows promise for applications in dual-frequency or dual-polarization active imaging.
- Accurate reconstruction of signals from correlation measurements is achievable.