Directional TGV-Based Image Restoration under Poisson Noise

Area of Science:

• Image processing
• Computational imaging
• Applied mathematics

Background:

• Directional images, common in microscopy and tomography, often suffer from noise and blur.
• Existing Directional Total Generalized Variation (DTGV) methods effectively handle impulse and Gaussian noise.
• Restoration of images with directional textures under Poisson noise remains a challenge.

Purpose of the Study:

• To extend the Directional Total Generalized Variation (DTGV) regularization for image restoration problems involving Poisson noise.
• To develop an improved technique for identifying the primary texture direction in directional images.
• To present an efficient and convergent algorithm for solving the proposed image restoration model.

Main Methods:

• Extension of DTGV regularization to incorporate generalized Kullback-Leibler divergence for Poisson noise fitting.
• Development of a novel method for precise texture direction identification.
• Application of an Alternating Direction Method of Multipliers (ADMM) algorithm with proven convergence properties.

Main Results:

• The proposed method effectively restores directional images corrupted by Poisson noise.
• The new texture direction identification technique enhances restoration accuracy.
• The ADMM algorithm provides exact solutions to subproblems with low computational cost.

Conclusions:

• The extended DTGV approach offers a robust solution for directional image restoration with Poisson noise.
• The improved texture direction detection significantly benefits image quality.
• The efficient ADMM implementation makes the method practical for real-world applications.