Machine learning has become the state-of-the-art in many fields including medical imaging. Using image denoising as an example, the training procedure typically involves a large number of noisy/clean image pairs. The mean squared error (MSE) between the noisy and clean images is minimized by a gradient descent algorithm such as Adaptive Moment Estimation (ADAM) algorithm. A routine pattern in a journal manuscript is as follows. Authors propose a new network architecture, the network is trained, and the results are compared with other methods in terms of peak signal-to-noise ratio (PSNR) and structure similarity (SSIM). This paper investigates whether it is suitable to train the network by directly optimizing PSNR or SSIM, instead of MSE. We claim that evaluation with PSNR or SSIM may not be proper for lesion detection tasks. We point out that PSNR is equivalent to the mean squared error method. Computer simulation results indicate the feasibility of using SSIM to train a network. The channelized Hotelling observer study shows that if lesions are not used in training the network, the network should not be used for lesion detection.