Deep neural network (DNN)-based image denoising methods have been proposed for use with medical images. These methods are commonly optimized and evaluated by use of traditional physical measures of image quality (IQ). However, the objective evaluation of IQ for such methods remains largely lacking. In this study, task-based IQ measures are used to evaluate the performance of DNN-based denoising methods. Specifically, we consider signal detection tasks under background-known-statistically conditions. The performance of the ideal observer (IO) and the Hotelling observer (HO) are quantified and detection efficiencies are computed to investigate the impact of the denoising operation on task performance. The experimental results show that, in the cases considered, the application of a denoising network generally results in a loss of task-relevant information. The impact of the depth of the denoising networks on task performance is also assessed. While mean squared error improved as the network depths were increased, signal detection performance degraded. These results highlight the need for the objective evaluation of IQ for DNN-based denoising technologies and may suggest future avenues for improving their effectiveness in medical imaging applications.