A non-transitory, machine readable storage medium encoded with computer program software, such that when a processor executes the computer program software, the processor performs a method for monitoring a positron emission tomography (PET) scanner performance during a continuous-bed-motion (CBM) acquisition mode, wherein the PET scanner has a patient bed that moves the axially short phantom in an axial motion through the PET scanner during the CBM acquisition, the method comprising:
- (a) generating time-of-flight (TOF) data of positron annihilation activity in the axially short phantom during the CBM acquisition, while accounting for the axial motion of the patient bed during the CBM acquisition, as a first data set that comprises CBM data y with spatial projection index j=(ρ,θ,ζ), wherein ρ is transaxial radial coordinate, θ is azimuthal coordinate, and TOF bin index T is modeled by combining true events modeled projection p from emission object f, defined by voxel index k, corrected for scanner efficiency through a normalization array n for attenuation by α, and scatter estimation S, corrected for scanner efficiency, and mean random data r according to:
- y
- _
- ρθζ
-
- T
- =
- a
- ρ
-
- θ
-
- ζ
-
- n
- ρθζ
- -
- 1
- (
- ε
- )
-
- ∑
- k
- C
- ρθζ
-
- T
- ,
- k
-
- f
- k
- +
- n
- ρθζ
- -
- 1
-
- S
- ρθζ
-
- T
- +
- r
- _
- ρθζ
-
- T
- =
- a
- ρ
-
- θ
-
- ζ
-
- n
- ρθ
-
- ζ
- -
- 1
- (
- ε
- )
-
- p
- _
- ρθζ
-
- T
- +
- n
- ρθζ
- -
- 1
-
- S
- ρθζ
-
- T
- +
- r
- _
- ρθζ
-
- T
- ;
- wherein C is the geometrical projection system matrix;
- wherein ε is the crystal efficiency;
- and
- wherein coordinate ζ is the CBM data normalization;
- (b) generating a complementary data set by integrating the TOF data over the axial motion of the patient bed during the CBM acquisition, wherein the complementary data set is modeled by the equation:
- y
- _
- ρθ
-
- zT
- =
- n
- ρθ
-
- z
- -
- 1
- (
- ε
- )
-
- B
- (
- a
- ρθζ
-
- ∑
- k
- C
- ρθζ
-
- T
- ,
- k
-
- f
- k
- )
- +
- n
- ρθ
-
- z
- -
- 1
- (
- ε
- )
-
- B
-
- (
- S
- ρθζ
-
- T
- )
- +
- r
- _
- ρθ
-
- zT
- =
- n
- ρθ
-
- z
- -
- 1
- (
- ε
- )
-
- p
- _
- ρθ
-
- zT
- +
-
- n
- ρθ
-
- z
- -
- 1
- (
- ε
- )
-
- S
- ρθ
-
- zT
- +
- r
- _
- ρθ
-
- zT
- ,
- wherein z is axial plane coordinate, B is a blurring operator defined as
- B
-
- (
- p
- _
- ρθζ
-
- T
- )
- =
- ∫
- 0
- t
- a
-
- c
-
- q
- ′
- dt
- ′
-
- ∑
- ζ
- e
- -
- λ
-
- t
-
- d
- ρθ
-
- z
- (
- t
- )
-
- p
- _
- ρθζ
-
- T
-
- δ
- z
- ,
- Z
-
- (
- ζ
- ,
- t
- )
- ,
- and y ρθz, a motion blurring operator, is calculated by:
- y
- ρθ
-
- z
- =
- B
-
- (
- y
- ρ
-
- θ
-
- ζ
- )
- =
- ∫
- 0
- t
- a
-
- c
-
- q
- ′
- dt
- ′
-
- ∑
- ζ
- e
- -
- λ
-
- t
-
- d
- ρθ
-
- z
- (
- t
- )
-
- y
- ρθζ
-
- δ
- z
- ,
- Z
-
- (
- ζ
- ,
- t
- )
- ,
- wherein t′acq is CBM acquisition time;
- and
- (c) simultaneously reconstructing the positron annihilation activity and crystal efficiency normalization coefficient from the complementary data set.