Application of information theory to the assessment of data integrity for coded aperture imaging

The SPECT imaging process has two fundamental stages: detection and display. The detection stage can be rigorously quantitatively described by Shannon's information theory. Information is transferred from the source to the detector in the photon emitting process. In the detection stage, integrity of projection data can be assessed by the information entropy, which is the conditional entropy standing for the average uncertainty of the source object under the condition of projection data. Simulations were performed to study projection data of emission computed tomography with a coded aperture collimator. Several types of coded aperture collimators were treated. Results demonstrate that the conditional entropy shows the data integrity, and indicate how the algorithms are matched or mismatched to the geometry. A new method for assessing data integrity is devised for those decision makers.