title: A randomization approach to handling data scaling in nuclear medicine.
abstract: OBJECTIVE
  In medical imaging, data scaling is sometimes desired to handle the system complexity, such as uniformity calibration. Since the data are usually saved in short integer, conventional data scaling will first scale the data in floating point format and then truncate or round the floating point data to short integer data. For example, when using truncation, scaling of 9 by 1.1 results in 9 and scaling of 10 by 1.1 results in 11. When the count level is low, such scaling may change the local data distribution and affect the intended application of the data.
  
  
  METHODS
  In this work, the authors use an example gated cardiac SPECT study to illustrate the effect of conventional scaling by factors of 1.1 and 1.2. The authors then scaled the data with the same scaling factors using a randomization approach, in which a random number evenly distributed between 0 and 1 is generated to determine how the floating point data will be saved as short integer data. If the random number is between 0 and 0.9, then 9.9 will be saved as 10, otherwise 9. In other words, the floating point value 9.9 will be saved in short integer value as 10 with 90% probability or 9 with 10% probability. For statistical analysis of the performance, the authors applied the conventional approach with rounding and the randomization approach to 50 consecutive gated studies from a clinical site.
  
  
  RESULTS
  For the example study, the image reconstructed from the original data showed an apparent perfusion defect at the apex of the myocardium. The defect size was noticeably changed by scaling with 1.1 and 1.2 using the conventional approaches with truncation and rounding. Using the randomization approach, in contrast, the images from the scaled data appeared identical to the original image. Line profile analysis of the scaled data showed that the randomization approach introduced the least change to the data as compared to the conventional approaches. For the 50 gated data sets, significantly more studies showed quantitative differences between the original images and the images from the data scaled by 1.2 using the rounding approach than the randomization approach [46/50 (92%) versus 3/50 (6%), p < 0.05]. Likewise, significantly more studies showed visually noticeable differences between the original images and the images from the data scaled by 1.2 using the rounding approach than randomization [29/50 (58%) versus 1/50 (2%), p < 0.05].
  
  
  CONCLUSIONS
  In conclusion, the proposed randomization approach minimizes the scaling-introduced local data change as compared to the conventional approaches. It is preferred for nuclear medicine data scaling.
authors.affiliation: Digirad Corporation, Poway, California 92064, USA. chbai@digirad.com
authors.forename: Chuanyong
authors.initials: C
authors.lastname: Bai
authors.forename: Richard
authors.initials: R
authors.lastname: Conwell
authors.forename: Joel
authors.initials: J
authors.lastname: Kindem
mesh_terms: D000465:Algorithms; D055424:Cardiac-Gated Imaging Techniques / Q000379:methods*; D003627:Data Interpretation, Statistical; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D015899:Tomography, Emission-Computed, Single-Photon / Q000379:methods*