The basic principles underlying a rigorous task-based approach to image quality are laid out in a sequence of four papers on Objective Assessment of Image Quality, or OAIQ for short:

• H. H. Barrett, “Objective assessment of image quality: effects of quantum noise and object variability”, J. Opt. Soc. Am. A, 7:1266-1278, 1990.
  
• H. H. Barrett, J. L. Denny, R. F. Wagner, and K. J. Myers, “Objective assessment of image quality: II. Fisher information, Fourier crosstalk, and figures of merit for task performance”, J. Opt. Soc. Am. A, 12, 5:834-852, 1995.
  
• H. H. Barrett, C. K. Abbey, and E. Clarkson, “Objective assessment of image quality: III. ROC metrics, ideal observers and likelihood-generating functions”, J. Opt. Soc. Am. A, 15:1520-1535, 1998.
  
• H. H. Barrett, K. J. Myers, N. Devaney, and J. C. Dainty, “Objective assessment of image quality: IV. Application to adaptive optics”, J. Opt. Soc. Am. A, 23:3080-3105, 2006.
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Reference

• A general reference on Objective Assessment of Image Quality is Barrett and Myers, Foundations of Image Science, and a recent tutorial by Kyle Myers can be found by clicking here.