The following probability density functions were computed for the ultrasound image of the carotid artery. The ultrasound noise coefficients were assumed to have a Gaussian distribution. The relationship between the extent of the noise probability density function and the clean signal probability density function is significant in determining the behavior of the coring function. The ideal coring function should modify the small values slightly, while large values should be mapped to the their same values.

Example of Well-Behaved Coring Function

Example of Distorted Coring Function

Example of the Majority of Coring Functions Assuming Noise Has Laplacian Distribution