Convex optimization-based windowed Fourier filtering with multiple windows for wrapped-phase denoising.

Area of Science:

• Image Processing
• Signal Analysis
• Computational Optics

Background:

• Windowed Fourier filtering (WFF) is effective for phase map denoising and fringe pattern analysis.
• Existing WFF methods suffer from high redundancy, computational cost, and challenges in window size selection.

Purpose of the Study:

• To propose an extended windowed Fourier filtering method for denoising wrapped-phase maps.
• To address the limitations of traditional WFF, including computational cost and window size selection.

Main Methods:

• Formulated as a convex optimization problem utilizing Gabor frames instead of windowed Fourier transform (WFT).
• Employed two Gabor frames with different window sizes simultaneously.
• Integrated a differential operator with a Gabor frame to preserve phase map discontinuities.

Main Results:

• Successfully resolved issues of high redundancy and computational cost associated with WFF.
• Demonstrated improved preservation of underlying phase map discontinuities.
• Achieved effective reconstruction of wrapped-phase maps even in severely contaminated scenarios.

Conclusions:

• The proposed Gabor frame-based method offers an efficient and robust solution for wrapped-phase map denoising.
• The integration of differential operators enhances the preservation of critical phase map features.
• This advanced technique shows significant potential for fringe pattern analysis in challenging conditions.