A Robust Wrap Reduction Algorithm for Fringe Projection Profilometry and Applications in Magnetic Resonance Imaging

Area of Science:

• Signal Processing
• Image Analysis

Background:

• 2D phase signals often contain 'wraps' that complicate analysis.
• Existing methods using Discrete Fourier Transform (DFT) have limitations, especially with non-integer frequency shifts and noise.

Purpose of the Study:

• To develop an effective algorithm for reducing wraps in 2D phase signals.
• To improve upon existing wrap reduction techniques, particularly for fringe projection profilometry (FPP).

Main Methods:

• Accurate estimation of the fundamental frequency of 2D complex signals using noise-robust methods.
• Removal of a dependent additive term from the phase map.
• Subtraction of a tilted plane from the phase signal, followed by re-wrapping, to handle non-integer frequency shifts.

Main Results:

• The proposed algorithm effectively reduces wraps in 2D phase signals.
• Demonstrated superior performance on FPP signals compared to state-of-the-art methods.
• Successfully cancels carrier effects and eliminates signal-wide slopes in FPP data.
• Shows effectiveness on carrier-free signals like MRI when inherent slopes are present.

Conclusions:

• The novel algorithm provides an effective solution for 2D phase signal wrap reduction.
• The method offers significant advantages for FPP applications, enhancing signal analysis.
• The noise-robust frequency estimation and phase manipulation techniques are key to its success.