Renal Perfusion and Hemodynamics: Accurate in Vivo Determination at CT with a 10-Fold Decrease in Radiation Dose and HYPR Noise Reduction1

© RSNA, 2009







 

Appendix E1

 

The working mechanism of HYPR-LR can be explained more clearly in frequency domain. The noisy images obtained by using the one-tenth dose level can be decomposed into multiple frequency components—the high-frequency portion and a low-frequency portion. Edges (ie, anatomic structures) and noise belong to the high-frequency portion, while the contrast information is conveyed primarily in the low-frequency portion. If the low-frequency component (ie, contrast signal) is kept narrow in time and the high-frequency component is averaged by using multiple frames, noise will be reduced without affecting the TAC substantially. Referring to Equation (E1), the operation of HYPR-LR can be divided into two parts: IC/(F ⊗ IC) and F ⊗ It, and expressed as

(E1)

If we take the logarithm of both sides of Equation (E1),

ln[IH (t)] = ln(IC ) – ln(F ⊗ IC) + ln(F ⊗ It),

(E2)

then it is clear that the effect of the first part IC/(F ⊗ IC) is equivalent to averaging high frequencies and the effect of the second part, F ⊗ It, is equivalent to low-pass filtering the individual frames. The averaged high frequencies and low-pass-filtered frequencies are added together to form the final noise-reduced image.

 

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