Fourier re-binning of time-of- flight positron emission tomography data

• US 20060266946A1
• Filed: 12/22/2005
• Published: 11/30/2006
• Est. Priority Date: 12/22/2004
• Status: Active Grant

• Current Assignee: Siemens Medical Solutions USA Incorporated (Siemens AG)
• Original Assignee: Siemens Medical Solutions USA Incorporated (Siemens AG)
• Inventors: Michel, Christian J., Casey, Michael E., Conti, Maurizio, Defrise, Michel
• Granted Patent: US 7,417,231 B2
• Time in Patent Office: Days
• US Class Current: 250/363.30
• CPC Class Codes: A61B 6/037 Emission tomography
• CPC Class Codes: G01T 1/2985 In depth localisation, e.g. using positron emitters; Tomographic imaging (longitudinal and transverse section imaging; apparatus for radiation diagnosis sequentially in different planes, steroscopic radiation diagnosis); using external radiation sources A61B6/02

Abstract

Fast reconstruction methods are provided for 3D time-of-flight (TOF) positron emission tomography (PET), based on 2D data re-binning. Starting from pre-corrected 3D TOF data, a re-binning algorithm estimates for each transaxial slice the 2D TOF sinogram. The re-binned sinograms can then be reconstructed using any algorithm for 2D TOF reconstruction. A TOF-FORE (Fourier re-binning of TOF data) algorithm is provided as an approximate re-binning algorithm obtained by extending the Fourier re-binning method for non-TOF data. In addition, two partial differential equations are identified that must be satisfied by consistent 3D TOF data, and are used to derive exact re-binning algorithms and to characterize the degree of the approximation in TOF-FORE. Numerical simulations demonstrate that TOF-FORE is more accurate than two different TOF extensions of the single-slice re-binning method, and suggest that TOF-FORE will be a valuable tool for practical TOF PET in the range of axial apertures and time resolutions typical of current scanners.

Claims

1. A method for reconstructing a nuclear medical image from TOF-PET imaging data, comprising the steps of:

obtaining three dimensional TOF-PET data from a PET scanner;

storing said TOF-PET data in a plurality of TOF time bins, each bin corresponding to a time difference value of photons arriving at opposite detectors of said PET scanner;

estimating, for each time bin, a two dimensional TOF sinogram of each transaxial slice z within an axial field of view of said scanner, by averaging independent estimates of redundant three dimensional TOF-PET data; and

reconstructing an image from said estimated two dimensional TOF sinograms using a two dimensional TOF reconstruction algorithm.

2. The method of claim 1, wherein said three dimensional TOF-PET data is represented by the following equation:

$p_t^m<br><br>\left(s,\mathrm{\varphi <br><br>},z,\mathrm{\delta <br><br>}\right)=\sqrt{1+{\mathrm{\delta <br><br>}}^2}<br><br>{\int <br><br>}_{-\mathrm{\infty <br><br>}}^{\mathrm{\infty <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>\mathrm{lf}<br><br>\left(s<br><br>\text{\hspace{1em}<br><br>}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\varphi <br><br>}-l<br><br>\text{\hspace{1em}<br><br>}<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\varphi <br><br>},s<br><br>\text{\hspace{1em}<br><br>}<br><br>\sin <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\varphi <br><br>}+l<br><br>\text{\hspace{1em}<br><br>}<br><br>\cos <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\varphi <br><br>},z+l<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\delta <br><br>}\right)<br><br>h<br><br>\left(t,l<br><br>\sqrt{1+{\mathrm{\delta <br><br>}}^2}\right)$

3. The method of claim 2, wherein the step of estimating comprises the step of modifying said three dimensional TOF-PET data to

$p_t$

( s , ϕ

, z , δ

) = ∫

- ∞

∞

⁢

 

⁢

ⅆ

lf ⁡

( s ⁢

 

⁢

cos ⁢

 

⁢

ϕ

- l ⁢

 

⁢

sin ⁢

 

⁢

ϕ

, s ⁢

 

⁢

sin ⁢

 

⁢

ϕ

+ l ⁢

 

⁢

cos ⁢

 

⁢

ϕ

, z + l ⁢

 

⁢

δ

) ⁢

h ⁡

( t , l ) .

4. The method of claim 3, wherein said modified data is estimated as

p_reb,t(s,φ

,z+tδ

)=p_t(s,φ

,z,δ

).

5. The method of claim 4, wherein said two dimensional TOF sinogram is obtained by solving for the equation

$p_{\mathrm{reb},t}$

( s , ϕ

, z ) ≃

1 2 ⁢

δ

max ⁡

( z ) ⁢

∫

- δ

max ⁡

( z ) δ

max ⁡

( z ) ⁢

ⅆ

δ

⁢

 

⁢

p t ⁡

( s , ϕ

, z , δ

) .

6. The method of claim 5, wherein said two dimensional TOF sinogram is obtained by solving for the equation

$P_t$

( ω

, k , z , δ

) ≃

P t ⁡

( ω

, k , z - k ⁢

 

⁢

δ

ω

, 0 ) .

7. The method of claim 5, wherein said two dimensional TOF sinogram is obtained by solving for the equation

$\begin{array}{c}{P}_t\end{array}$

( ω

, k , z 0 , 0 ) = ⁢

P t ⁡

( ω

, k , z 1 , δ

1 ) - ∫

0 δ

1 ⁢

ⅆ

δ

⁢

ⅆ

P t ⁡

( ω

, k , z 0 + k ⁢

 

⁢

δ

/ ω

, δ

) ⅆ

δ

= ⁢

P t ⁡

( ω

, k , z 0 + k ⁢

 

⁢

δ

1 / ω

, δ

1 ) + ⁢

1 ω

⁢

∫

0 δ

1 ⁢

ⅆ

δ

⁡

( δ

⁢

∂

3 ⁢

P t ∂

ω

⁢

∂

z 2 + t σ

2 ⁢

∂

2 ⁢

P t ∂

ω

⁢

∂

z - 1 σ

2 ⁢

∂

2 ⁢

P t ∂

ω

⁢

∂

δ

) ⁢

( ω

, k , z 0 + k ⁢

 

⁢

δ

ω

, δ

) .

8. The method of claim 5, wherein said two dimensional TOF sinogram is obtained by solving for the equation

$p_t$

( s , ϕ

, z 0 , 0 ) = p t ⁡

( s , ϕ

, z 0 - t ⁢

 

⁢

δ

1 , δ

1 ) - σ

2 ⁢

∫

0 δ

1 ⁢

ⅆ

δ

⁢

∂

2 ⁢

p t ⁡

( s , ϕ

, z 0 - t ⁢

 

⁢

δ

, δ

) ∂

z ⁢

∂

t .