Method and apparatus for using image cumulative distribution function for tomographic reconstruction quality control

1. A method for quality control in image space for processing with an input data set, the method performed on a processor comprising:

providing an image object and the input data set, the image object including a plurality of voxels;

determining a data model from the image object;

determining a cumulative distribution function (CDF) for the input data set from the data model and the input data set based on a plurality of projections;

transforming the CDF to an image cumulative distribution function (ICDF) in image space, the ICDF representing a number of standard deviations associated with each voxel of the image object; and

displaying an output of the ICDF.

2. The method of claim 1 , wherein the image object is a three dimensional (3D) image object.

3. The method of claim 1 , wherein the image object is a two dimensional (2D) image object.

4. The method of claim 1 , wherein the CDF is a modified Poisson cumulative distribution function (MCDF).

5. The method of claim 1 , wherein displaying the output of the ICDF includes displaying a slice of the output of the ICDF as a plurality of pixels, each pixel representing an ICDF value of a corresponding voxel of the image object.

6. The method of claim 5 , wherein the slice is a two dimensional (2D) slice.

7. The method of claim 5 , wherein displaying the slice includes displaying the ICDF in color with a plurality of colors representing a plurality of values of respective pixels.

8. The method of claim 5 , further including automatically determining whether the image object satisfies a predetermined quality control criterion based on the ICDF.

9. The method of claim 8 , wherein automatically determining whether the image object satisfies the predetermined quality control criterion includes determining whether any pixel has an ICDF value exceeding a predetermined threshold in magnitude.

10. The method of claim 8 , wherein automatically determining whether the image object satisfies the predetermined quality control criterion includes automatically comparing a magnitude of an average ICDF value of the pixels to a predetermined mean threshold.

11. The method of claim 8 , wherein automatically determining whether the image object satisfies the predetermined quality control criterion includes automatically comparing a variance of ICDF values of the pixels to a predetermined variance threshold.

12. The method of claim 1 , wherein transforming the CDF to the ICDF comprises:

de-meaning the CDF;

back projecting the de-meaned CDF to image space; and

normalizing the back projected de-meaned CDF to unit variance.

13. The method of claim 12 , wherein normalizing the back projected de-meaned CDF comprises:

computing amounts contributed by respective projections to a back projection of a uniform distribution function;

adding squared amounts contributed by respective projections to estimate a total variance; and

dividing the back projected de-meaned CDF by a square root of the estimated total variance.

14. The method of claim 13 , wherein under a null hypothesis for the data model, the uniform distribution function is uniformly distributed between −0.5 and 0.5.

15. A nuclear imaging device for providing quality control in image space for processing with an input data set, the device comprising:

a detector unit configured to detect radiation emitted from within a detecting area and provide an input data set indicative of the detected radiation;

a tomographic reconstruction unit configured to provide an image object using the input data set, the image object including a plurality of voxels;

an image cumulative distribution function (ICDF) module configured to transform a cumulative distribution function (CDF) for the input data set in data space to an image cumulative distribution function (ICDF) in image space, the ICDF representing a number of standard deviations associated with each voxel of the image object; and

an output port configured for outputting the image object and the ICDF.

16. The nuclear imaging device of claim 15 , wherein the image object is a three dimensional (3D) image object.

17. The nuclear imaging device of claim 15 , wherein the CDF is a modified Poisson cumulative distribution function (MCDF).

18. The nuclear imaging device of claim 15 , wherein the output port is configured to display a slice of the ICDF output as a plurality of pixels, each pixel representing an ICDF value of a corresponding voxel of the image object.

19. The nuclear image device of claim 15 , wherein the ICDF module is further configured to automatically determine whether the image object satisfies a predetermined quality control criterion based on the ICDF.

20. The nuclear imaging device of claim 15 , wherein the ICDF module is configured to transform the CDF to the ICDF by:

de-meaning the CDF;

back projecting the de-meaned CDF to image space; and

normalizing the back projected de-meaned CDF to unit variance.

21. The nuclear imaging device of claim 15 , wherein the detector unit includes a single photon computed tomography detector.

22. The nuclear imaging device of claim 15 , wherein the detector unit includes a positron emission tomography detector.

23. A computer readable non-transitory storage medium having instructions tangibly embodied thereon, the instructions when executed by a computer processor causing the processor to perform the operations of:

providing an image object and an input data set, the image object including a plurality of voxels;

determining a data model from the image object;

determining a cumulative distribution function (CDF) for the input data set from the data model and the input data set based on a plurality of projections;

transforming the CDF to an image cumulative distribution function (ICDF) in image space, the ICDF representing a number of standard deviations associated with each voxel of the image object; and

displaying an output of the ICDF.