If the activation function of the output layer of the AE is a sigmoid function, thus limiting neuron outputs to be between 0 and 1, and the input features are normalized to be between 0 and 1 we can use as loss function the binary cross-entropy. This cots/loss function is typically used in classification problems, but it works well for autoencoders. The formula for it is
$$ L_{\textrm{CE}} = -\frac{1}{n}\sum_{i = 1}^{n}\sum_{j = 1}^{p}[x_{j,i} \log\tilde{x}_{j,i}+\left(1-x_{j,i}\right)\log (1-\tilde{x}_{j,i})]. $$