Apparatus and method for smoothing random event data obtained from a Positron Emission Tomography scanner

An apparatus for smoothing random event data obtained from a Positron Emission Tomography (PET) scanner, the apparatus comprising:

• a processing circuit configured to
• obtain initial random event data u(s, φ, t=0)=u0(s, φ), corresponding to t=0, the initial random event data corresponding to lines-of-responses of the PET scanner,
• calculate second-order central differences uss, uφφ with respect to s, φ;
• calculate a gradient ut, using ut=2(uss+uφφ)−λ(u−u0), where λ is a constant parameter,
• update the random event data using u(s, φ, t2)=u(s, φ, t1)+Δt ut, where Δt=t2−t1, t1=0 in a first iteration, and Δt is greater than 0, and
• repeat the 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.

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, z, θ, t=0)=u0(s, φ, z, θ), corresponding to t=0, the initial random event data corresponding to lines-of-responses of the PET scanner;
• calculating second-order central differences uss, uφφ, uzz, uθθ, with respect to s, φ, z, θ;
• calculating a gradient ut, using ut=2(uss+uφφ+uzz+uθθ)−λ(u−u0), where λ is a constant parameter;
• updating the random event data using u(s, φ, z, θ, t2)=u(s, φ, z, θ, t1)+Δt ut, where Δt=t2−t1, t1=0 in a first iteration, and Δt is greater than 0;
• and
• repeating 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, z, θ, t) from a previous iteration is less than a predetermined threshold value.

An apparatus for smoothing random event data obtained from a Positron Emission Tomography (PET) scanner, the method comprising:

• a processing circuit configured to
• obtain initial random event data u(s, φ, z, θ, t=0)=u0(s, φ, z, θ), corresponding to t=0, the initial random event data corresponding to lines-of-responses of the PET scanner;
• calculate second-order central differences uss, uφφ, uzz, uθθ, with respect to s, φ, z, θ;
• calculate a gradient ut, using ut=2(uss+uφφ+uzz+uθθ)−λ(u−u0), where λ is a constant parameter;
• update the random event data using u(s, φ, z, θ, t2)=u(s, φ, z, θ, t1)+Δt ut, where Δt=t2−t1, t1=0 in a first iteration, and Δt is greater than 0;
• and
• repeat the calculating the second-order central differences, calculating the gradient, and updating the random event data until a change in u(s, φ, z, θ, t) from a previous iteration is less than a predetermined threshold value.