Relating Fisher Information to Detectability of Changes in Nodule Characteristics with CT
Fisher information provides a bound on the variance of any unbiased estimate for estimation tasks involving nonrandom parameters. In addition, a Fisher information approximation for ideal-observer detectability has been derived. We adopt and generalize such an approximation to establish a method to assess a system’s ability to detect small changes in lesion characteristics. By representing the lesion by a size parameter, the ability to detect small changes can be approximated by a function involving the size difference and the Fisher information. A concept, termed the approximated least required difference (ALRD), is introduced and evaluated as an upper bound for assessing a system’s power in size discrimination. We present a simulation study for lung nodules as an example to illustrate such a framework, where the image model incorporates a simulated CT imaging system, a thorax background and parameterized nodules. The noise is assumed to be multivariate Gaussian and the noise power spectrum (NPS) method is used to estimate the covariance matrix for the Fisher information calculation. In addition to bounding performance, our results also provide insights into factors, including nodule characteristics and acquisition parameters, that influence ALRD performance. This framework can be extended to connect other discrimination and estimation tasks, facilitating objective assessment and optimization of quantitative imaging systems.
KeywordsFisher Information Lung Nodule Nodule Size Estimation Task Nodule Characteristic
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- 1.Eisenhauer, E.A., Therasse, P., Bogaerts, J., Schwartz, L.H., Sargent, D., Ford, R., Dancey, J., Arbuck, S., Gwyther, S., Mooney, M., Rubinstein, L., Shankar, L., Dodd, L., Kaplan, R., Lacombe, D., Verweij, J.: New response evaluation criteria in solid tumors: revised RECIST guideline (version 1.1). European Journal of Cancer 45(2), 228–247 (2009)CrossRefGoogle Scholar
- 4.Gavrielides, M.A., Kinnard, L.M., Myers, K.J., Peregoy, J., Pritchard, W.F., Zeng, R., Esparza, J., Karanian, J., Petrick, N.: A resource for the assessment of lung nodule size estimation methods: database of thoracic CT scans of an anthropomorphic phantom. Optics Express 18, 15244–15255 (2010)CrossRefGoogle Scholar
- 5.Van Trees, H.L.: Detection, Estimation, and Modulation Theory, Part I. Wiley (1968)Google Scholar
- 6.Amari, S.I.: Differential geometrical theory of statistics. Springer (1985)Google Scholar
- 7.Barret, H.H., Myers, K.J.: Foundations of Image Science. Wiley (2004)Google Scholar
- 10.Hsieh, J.: Computed Tomography: Principles, Design, Artifacts and Recent Advances. SPIE Press, Bellingham (2003)Google Scholar
- 11.Zeng, R., Petrick, N., Gavrielides, M.A., Myers, K.J.: Approximations of noise covariance in multi-slice helical CT scans: impact on lung nodule size estimation. Med. Phys. 56, 6223–6242 (2011)Google Scholar