Multiscale Tikhonov-Total Variation Image Restoration Using Spatially Varying Edge Coherence Exponent

Area of Science:

• Image Processing
• Computer Vision
• Applied Mathematics

Background:

• Partial differential equation (PDE)-based regularization is widely used for image restoration.
• Existing methods struggle with adapting to local structures, leading to over-smoothing and staircasing artifacts.

Purpose of the Study:

• To propose a novel spatially adaptive multiscale variable exponent-based anisotropic variational PDE method.
• To overcome limitations of current methods by enhancing edge structures and reducing artifacts.

Main Methods:

• Incorporating a spatially varying edge coherence exponent map derived from structure tensor eigenvalues.
• Developing a multiscale exponent model to balance Tikhonov and total variation (TV) regularization.
• Mathematical analysis ensuring existence of a minimizer and properties in variable exponent space.
• Discretization satisfying the maximum-minimum principle to prevent artificial edge creation.

Main Results:

• The proposed multiscale Tikhonov-TV (MTTV) method preserves edges effectively and provides selective denoising.
• It successfully mitigates over-smoothing and staircasing artifacts for both additive and multiplicative noise.
• Experimental results show superior performance compared to contemporary denoising algorithms in signal-to-noise ratio improvement and structure preservation.

Conclusions:

• The developed MTTV method offers a significant advancement in image restoration, particularly for edge preservation and artifact reduction.
• The approach demonstrates robustness across various noise models and image types.
• Future extensions for multiplicative noise and multichannel imagery are promising.