Systems and methods of artifact reduction in magnetic resonance images
US-2024410966-A1 · Dec 12, 2024 · US
US8942452B2 · US · B2
| Field | Value |
|---|---|
| Publication number | US-8942452-B2 |
| Application number | US-201213475584-A |
| Country | US |
| Kind code | B2 |
| Filing date | May 18, 2012 |
| Priority date | May 18, 2012 |
| Publication date | Jan 27, 2015 |
| Grant date | Jan 27, 2015 |
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A method and apparatus for smoothing random event data obtained from a Positron Emission Tomography (PET) scanner. The method includes obtaining initial random event data u(s, φ, t=0)=u 0 (s, φ), corresponding to t=0, calculating second-order central differences u ss , u φφ with respect to s, φ, calculating a gradient u t , using u t =2(u ss +u φφ )−λ(u−u 0 ), where λ is a constant parameter, and updating the random event data using u(s, φ, t 2 )=u(s, φ, t 1 )+Δt u t , where Δt=t 2 −t 1 , t 1 =0 in a first iteration, and Δt is greater than 0. The method repeats the steps of calculating the second-order central differences, calculating the gradient, and updating the random event data until a change in u(s, φ, t) from a previous iteration is less than a predetermined threshold value.
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The invention claimed is: 1. A method for smoothing random event data obtained from a Positron Emission Tomography (PET) scanner, the method comprising: obtaining initial random event data u(s, φ, t=0)=u 0 (s, φ), corresponding to t=0, the initial random event data corresponding to line-of-responses of the PET scanner; calculating second-order central differences u ss , u φφ with respect to s, φ; calculating a gradient u t , using u t =2(u ss +u φφ )−λ(u−u 0 ), where λ is a c…
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