This paper addresses issues in the calculation of a detectability measure for the ideal linear (Hotelling) observer performing a detection task on a digital radiograph. The main computational problem is that the inverse of a very large covariance matrix is required. The conventional approach is to assume some form of stationarity and argue that the matrix is diagonalized by discrete Fourier transformation, but there are many reasons why this assumption is unrealistic. After a brief review of the underlying mathematics, we present several practical algorithms for computing the detectability and some hints as to when each is applicable. The main conclusion is that large matrices should not be feared.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.