Optimal energy weighting of dark field signal in differential phase contrast X-ray imaging

1. A signal processing apparatus, comprising:

a memory that stores a plurality of instructions; and

a processor coupled to the memory and configured to execute the plurality of instructions to:

receive dark-field signal data for different energy channels, the dark-field signal data corresponding to signals detected, in different energy channels, after exposure to X-ray radiation from an X-ray source;

logarithmize the dark-field signal data to obtain log-dark-field signal data;

transform the log-dark-field signal data via linear transformation when the plurality of instructions include performing optional linear transformation;

integrate the linearly transformed log-dark-field signal data or the log-dark-field signal data of at least two energy channels into an energy weighted log-dark-field signal by using energy weights corresponding to the at least two energy channels, and

output said energy weighted log-dark-field signal.

2. The signal processing apparatus as per claim 1 , wherein the energy weights include a respective energy term that can be expressed in the form E p with p<−2.

3. The signal processing apparatus as per claim 2 , wherein −4≤p<−2.

4. The signal processing apparatus as per claim 1 , wherein the detected signals correspond to projection data, and the processor is further configured to execute the plurality of instructions to extract, for at least two energy channels, from intensity data, the respective dark-field signal data, the intensity data being derived from the projection data.

5. The signal processing apparatus as per claim 1 , wherein the energy weights include respective energy terms, at least one of the energy terms having an energy value as an exponent.

6. The signal processing apparatus as per claim 5 , wherein the energy weights include respective energy terms of the form

a

E

i

2

*

(

1

-

exp

⁡

(

-

b

⁡

(

E

⁢

0

E

i

2

)

2

)

,

wherein

a is an arbitrary constant,

b is a constant that relates to an internal structure of an imaged object,

E 0 is a design energy, and

E i are energy levels for the different energy channels i.

7. The signal processing apparatus as per claim 1 , wherein the optional linear transformation is performed by any one of:

(i) a high pass filter or a low-pass filter or

(ii) a backward-projection operator.

8. The signal processing apparatus as per claim 1 , wherein the processor is further configured to execute the plurality of instructions to apply a bias correction to dark field projection data corresponding to the received dark-field signal data.

9. An imaging system, comprising:

a detector;

an X-ray source; and

a signal processing apparatus including:

a memory that stores a plurality of instructions; and

a processor coupled to the memory and configured to execute the plurality of instructions to:

receive dark-field signal data for different energy channels, the dark-field signal data corresponding to signals detected, in different energy channels, at the detector after exposure to X-ray radiation from the X-ray source;

logarithmize the dark-field signal data to obtain log-dark-field signal data;

transform the log-dark-field signal data via linear transformation when the plurality of instructions include performing optional linear transformation;

integrate the linearly transformed log-dark-field signal data or the log-dark-field signal data of at least two energy channels into an energy weighted log-dark-field signal by using energy weights corresponding to the at least two energy channels, and

output said energy weighted log-dark-field signal.

10. The imaging system as per claim 9 , wherein the imaging system is a computed tomography (CT) scanner or a planar projection X-ray imager.

11. The imaging system as per claim 9 , wherein

i) the detector is an energy resolving detector, and the different energy channels correspond to different energy values of the energy resolving detector; or

ii) the detector is an energy integrating detector, and the different energy channels correspond to detector readings for X-ray exposures by the X-ray source at different voltage levels.

12. A signal processing method, comprising:

receiving, for different energy channels, respective dark-field signal data, the dark-field signal data corresponding to signals detected, in the different energy channels, after exposure to X-ray radiation from an X-ray source;

logarithmizing the dark-field signal data to obtain log-dark-field signal data;

optionally, linearly transforming the log-dark-field signal data;

integrating the log-dark-field signal data or the linearly transformed log-dark-field signal data of at least two energy channels into an energy weighted log-dark-field signal by using energy weights corresponding to the at least two energy channels; and

outputting said energy weighted log-dark-field signal.

13. The signal processing method as per claim 12 , wherein the energy weights include a respective energy term that can be expressed in the form E p with p<−2.

14. A non-transitory computer-readable medium storing computer-readable instructions, which, when being executed by a processor, cause the processor to perform a signal processing method comprising:

receiving, for different energy channels, respective dark-field signal data, the dark-field signal data corresponding to signals detected, in the different energy channels, after exposure to X-ray radiation from an X-ray source;

logarithmizing the dark-field signal data to obtain log-dark-field signal data;

optionally, linearly transforming the log-dark-field signal data;

integrating the log-dark-field signal data or the linearly transformed log-dark-field signal data of at least two energy channels into an energy weighted log-dark-field signal by using energy weights corresponding to the at least two energy channels; and

outputting said energy weighted log-dark-field signal.