Spectrograms offer a time-frequency representation well-suited for audio analysis, where structured signals manifest as horizontal or vertical patterns and noise appears as irregular textures. In this paper, we propose a spectrogram denoising method based on mathematical morphology, and more precisely on max-trees. We treat the spectrogram as a grayscale image and apply a sequence of filters on its max-tree representation. We propose a method to isolate signal regions by filtering components according to contrast and shape. A binary mask is constructed from the remaining components, which is used to reconstruct the denoised signal by inverting the masked short-time Fourier transform (STFT). The method is highly interpretable and preserves the signal structure while effectively removing noise. We demonstrate its effectiveness on synthetic and real audio signals.