Image decomposition model Shearlet-Hilbert-L² with better performance for denoising in ESPI fringe patterns

Area of Science:

• Optical Engineering
• Image Processing
• Signal Processing

Background:

• Electronic Speckle Pattern Interferometry (ESPI) is crucial for measuring surface deformations.
• ESPI fringe patterns often suffer from noise, hindering accurate analysis.
• Existing denoising methods have limitations in handling diverse fringe densities and noise levels.

Purpose of the Study:

• To propose a novel image decomposition model for enhanced denoising of ESPI fringe patterns.
• To improve the performance of noise reduction in ESPI images with varying fringe densities.
• To offer a superior alternative to current state-of-the-art denoising techniques.

Main Methods:

• Developed the Shearlet-Hilbert-L² model for image decomposition.
• Utilized shearlet smoothness spaces for low-density fringes.
• Employed adaptive Hilbert space for high-density fringes and L² space for noise.
• Leveraged the directional sensitivity of the shearlet transform.

Main Results:

• The Shearlet-Hilbert-L² model demonstrated superior denoising performance across various ESPI fringe patterns.
• Effective filtering of uniform, moderately variable, and greatly variable density fringe patterns was achieved.
• The model outperformed windowed Fourier filtering and coherence-enhancing diffusion methods.
• Comparison with the BL-Hilbert-L² model showed improved results.

Conclusions:

• The proposed Shearlet-Hilbert-L² model offers a robust and effective solution for denoising ESPI fringe patterns.
• Its ability to handle diverse fringe densities and noise conditions makes it highly valuable.
• This advancement contributes significantly to the accuracy and reliability of ESPI measurements.