1. Lecture 23: 1. MRI noise processes MP574

2. Dipole Moments from Entire Sample Magnetic Field (B 0 ) Positive Orientation Negative Orientation Magnetic Field (B 0 )  

3. Source of Signal Proton or Water MRI –B o Magnetic Field –Proton Nucleus S = ±ħ/2 EE oz B kT ME 4 22   

4. Detected Signal )sin() )()( )cos( 2 1 tg kT Ah tg kT BAh tStV tgAB L L LL o L        x y z B 1 (t)

5. Brownian Motion http://en.wikipedia.org/wiki/Wiener_process Brownian Motion Conditions: x 0 = 0 x(t) is a continuous random variable Increments x(t 1 ) and x(t 2 ) are statistically independent and normally distributed

6. Brownian Motion

7. Johnson or “Thermal” Noise RpRp RcRc Patient Resistance Electrical Resistance of Coil Thermal noise in patient dominant at high field strengths

8. Johnson or “Thermal” Noise on both I and Q channels I = “in phase” Q = “quadrature” or 90 o out of phase Imaginary Real

9. Independent Realizations of GWN on each of the I,Q channels Imaginary Real

10. Background noise Imaginary Real

11. Rayleigh and Rician Probability Distribution Functions

12. High SNR

13. Dependence on SNR