We investigate the detectability of breast cone beam computed tomography images using human and model observers and the variations of exponent, β, of the inverse power-law spectrum for various reconstruction filters and interpolation methods in the Feldkamp-Davis-Kress (FDK) reconstruction. Using computer simulation, a breast volume with a 50% volume glandular fraction and a 2 mm diameter lesion are generated and projection data are acquired. In the FDK reconstruction, projection data are apodized using one of three reconstruction filters; Hanning, Shepp-Logan, or Ram-Lak, and back-projection is performed with and without Fourier interpolation. We conduct signal-known-exactly and background-known-statistically detection tasks. Detectability is evaluated by human observers and their performance is compared with anthropomorphic model observers (a non-prewhitening observer with eye filter (NPWE) and a channelized Hotelling observer with either Gabor channels or dense difference-of-Gaussian channels). Our results show that the NPWE observer with a peak frequency of 7 cyc/ degree attains the best correlation with human observers for the various reconstruction filters and interpolation methods. We also discover that breast images with smaller β do not yield higher detectability in the presence of quantum noise.