Supervised learning is a mainstream approach to audio signal enhancement (SE) and requires parallel training data consisting of both noisy signals and the corresponding clean signals. Such data can only be synthesised and are mismatched with real data, which can result in poor performance on real data. Moreover, clean signals may be inaccessible in certain scenarios, which renders this conventional approach infeasible. Here we explore SE using non-parallel training data consisting of noisy signals and noise, which can be easily recorded. We define the positive (P) and the negative (N) classes as signal inactivity and activity, respectively. We observe that the spectrogram patches of noise clips can be used as P data and those of noisy signal clips as unlabelled data. Thus, learning from positive and unlabelled data enables a convolutional neural network to learn to classify each spectrogram patch as P or N to enable SE.