Total variation applied to Compted Tomography

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Total variation applied to Compted Tomography

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Total variation (TV) is a powerful mathematical tool used in computed tomography (CT) to enhance image reconstruction by reducing noise while preserving sharp edges. In CT imaging, reconstructed images often suffer from artifacts and noise due to limited projection data or low-dose scanning. TV regularization addresses these issues by penalizing high-frequency variations in the image while maintaining structural details.

The core idea is to minimize the total variation of the image, which measures the sum of absolute gradients. This approach favors piecewise-constant solutions, effectively smoothing noise without blurring edges. In CT reconstruction, TV is often combined with iterative optimization techniques like gradient descent or compressed sensing algorithms to refine the image iteratively.

One key advantage of TV in CT is its ability to produce high-quality reconstructions even with fewer projections, reducing radiation exposure for patients. However, challenges include computational cost and potential over-smoothing of fine textures. Advanced variations like weighted TV or anisotropic TV have been developed to address these limitations while maintaining reconstruction accuracy.

By incorporating TV regularization, CT imaging achieves a balance between noise suppression and edge preservation, making it particularly useful in low-dose and sparse-view CT applications.