Total Variation Applied to Computed Tomography Imaging

The primary focus of this research involves applying total variation regularization to computed tomography (CT) imaging. Computed tomography is a medical imaging technique that creates three-dimensional images through X-ray scanning of the human body. In conventional CT imaging, artifacts and noise may occur during reconstruction due to differential X-ray absorption by tissues and bones of varying densities. Implementing total variation minimization in CT reconstruction algorithms helps reduce these artifacts and noise, resulting in clearer and more accurate images that assist physicians in making better diagnostic decisions.

From a computational perspective, total variation regularization can be implemented through gradient descent methods or proximal algorithms, where the TV term penalizes abrupt intensity changes in the reconstructed image. The core optimization problem typically involves minimizing a cost function combining data fidelity and TV regularization terms:

min_x ||Ax - b||²₂ + λTV(x)

where A represents the system matrix, b denotes projection data, and λ controls the regularization strength. The study also explores parameter tuning strategies for the regularization parameter λ to further optimize imaging results, providing new methodologies for future computed tomography research. Implementation often utilizes iterative algorithms like split Bregman or alternating direction method of multipliers (ADMM) for efficient TV minimization.