title: Image simulation and a model of noise power spectra across a range of mammographic beam qualities.
abstract: OBJECTIVE
  The aim of this work is to create a model to predict the noise power spectra (NPS) for a range of mammographic radiographic factors. The noise model was necessary to degrade images acquired on one system to match the image quality of different systems for a range of beam qualities.
  
  
  METHODS
  Five detectors and x-ray systems [Hologic Selenia (ASEh), Carestream computed radiography CR900 (CRc), GE Essential (CSI), Carestream NIP (NIPc), and Siemens Inspiration (ASEs)] were characterized for this study. The signal transfer property was measured as the pixel value against absorbed energy per unit area (E) at a reference beam quality of 28 kV, Mo/Mo or 29 kV, W/Rh with 45 mm polymethyl methacrylate (PMMA) at the tube head. The contributions of the three noise sources (electronic, quantum, and structure) to the NPS were calculated by fitting a quadratic at each spatial frequency of the NPS against E. A quantum noise correction factor which was dependent on beam quality was quantified using a set of images acquired over a range of radiographic factors with different thicknesses of PMMA. The noise model was tested for images acquired at 26 kV, Mo/Mo with 20 mm PMMA and 34 kV, Mo/Rh with 70 mm PMMA for three detectors (ASEh, CRc, and CSI) over a range of exposures. The NPS were modeled with and without the noise correction factor and compared with the measured NPS. A previous method for adapting an image to appear as if acquired on a different system was modified to allow the reference beam quality to be different from the beam quality of the image. The method was validated by adapting the ASEh flat field images with two thicknesses of PMMA (20 and 70 mm) to appear with the imaging characteristics of the CSI and CRc systems.
  
  
  RESULTS
  The quantum noise correction factor rises with higher beam qualities, except for CR systems at high spatial frequencies, where a flat response was found against mean photon energy. This is due to the dominance of secondary quantum noise in CR. The use of the quantum noise correction factor reduced the difference from the model to the real NPS to generally within 4%. The use of the quantum noise correction improved the conversion of ASEh image to CRc image but had no difference for the conversion to CSI images.
  
  
  CONCLUSIONS
  A practical method for estimating the NPS at any dose and over a range of beam qualities for mammography has been demonstrated. The noise model was incorporated into a methodology for converting an image to appear as if acquired on a different detector. The method can now be extended to work for a wide range of beam qualities and can be applied to the conversion of mammograms.
authors.affiliation: National Coordinating Centre for the Physics of Mammography, Royal Surrey County Hospital, Guildford GU2 7XX, United Kingdom and Department of Physics, University of Surrey, Guildford GU2 7XH, United Kingdom.
authors.forename: Alistair
authors.initials: A
authors.lastname: Mackenzie
authors.affiliation: National Coordinating Centre for the Physics of Mammography, Royal Surrey County Hospital, Guildford GU2 7XX, United Kingdom and Department of Physics, University of Surrey, Guildford GU2 7XH, United Kingdom.
authors.forename: David R
authors.initials: DR
authors.lastname: Dance
authors.affiliation: Centre for Vision, Speech and Signal Processing, Faculty of Engineering and Physical Sciences, University of Surrey, Guildford GU2 7XH, United Kingdom and Computer Vision and Robotics Research Institute, University of Girona, Girona 17071, Spain.
authors.forename: Oliver
authors.initials: O
authors.lastname: Diaz
authors.affiliation: National Coordinating Centre for the Physics of Mammography, Royal Surrey County Hospital, Guildford GU2 7XX, United Kingdom and Department of Physics, University of Surrey, Guildford GU2 7XH, United Kingdom.
authors.forename: Kenneth C
authors.initials: KC
authors.lastname: Young
mesh_terms: D055592:Biophysical Phenomena; D001943:Breast Neoplasms / Q000000981:diagnostic imaging; D005260:Female; D006801:Humans; D008327:Mammography / Q000592:standards / Q000706:statistics & numerical data*; D015233:Models, Statistical; D019047:Phantoms, Imaging / Q000592:standards / Q000706:statistics & numerical data; D019904:Polymethyl Methacrylate; D011856:Radiographic Image Enhancement / Q000379:methods* / Q000592:standards; D012815:Signal Processing, Computer-Assisted; D059629:Signal-To-Noise Ratio
chemical_list: D019904:Polymethyl Methacrylate