Signal reconstruction from noisy-phase and -magnitude data

Area of Science:

• Signal Processing
• Fourier Analysis
• Data Reconstruction

Background:

• Signal reconstruction from partial Fourier transform information (magnitude or phase) is crucial for various applications.
• Existing methods struggle with reconstructing signals from noisy magnitude and phase data simultaneously.

Purpose of the Study:

• To develop a novel signal reconstruction algorithm addressing noisy magnitude and phase data.
• To introduce and analyze spectral prototype constraint sets for improved reconstruction accuracy.

Main Methods:

• Developing a reconstruction algorithm that accounts for deviations in magnitude and phase estimates.
• Defining and analyzing new spectral prototype constraint sets for Fourier transform magnitude and phase.
• Constructing corresponding projection operators for the defined constraint sets.

Main Results:

• The proposed spectral prototype constraint sets effectively handle deviations in noisy magnitude and phase data.
• Simulation results demonstrate enhanced performance in signal reconstruction compared to existing methods.
• The developed projection operators facilitate the application of these constraint sets.

Conclusions:

• The novel approach using spectral prototype constraints offers a significant improvement for signal reconstruction from noisy Fourier transform data.
• This method provides a robust solution for applications requiring accurate signal recovery under noisy conditions.