SNR and noise measurements for medical imaging: I. A practical approach based on statistical decision theory

A method of measuring the image quality of medical imaging equipment is considered within the framework of statistical decision theory. In this approach, images are regarded as random vectors and image quality is defined in the context of the image information available for performing a specified detection or discrimination task. The approach provides a means of measuring image quality, as related to the detection of an image detail of interest, without reference to the actual physical mechanisms involved in image formation and without separate measurements of signal transfer characteristics or image noise. The measurement does not, however, consider deterministic errors in the image; they need a separate evaluation for imaging modalities where they are of concern. The detectability of an image detail can be expressed in terms of the ideal observer's signal-to-noise ratio (SNR) at the decision level. Often a good approximation to this SNR can be obtained by employing sub-optimal observers, whose performance correlates well with the performance of human observers as well. In this paper the measurement of SNR is based on implementing algorithmic realizations of specified observers and analysing their responses while actually performing a specified detection task of interest. Three observers are considered: the ideal prewhitening matched filter, the non-prewhitening matched filter, and the DC-suppressing non-prewhitening matched filter. The construction of the ideal observer requires an impractical amount of data and computing, except for the most simple imaging situations. Therefore, the utilization of sub-optimal observers is advised and their performance in detecting a specified signal is discussed. Measurement of noise and SNR has been extended to include temporally varying images and dynamic imaging systems.