and the goal is to minimize the loss between $O_t$ and $A_t$.

Spectrogram Inpainting Model
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For our spectrogram inpainting models, we first transform each the $A_t$ into a spectrogram $S_t$ by short-time Fourier transform (STFT) with window width $\omega$, treat it as a special image and thereby considering audio inpainting problem as a special image inpainting problem to recover the missing parts in the spectrogram. Then the recovered spectrogram will be transformed back to waveform as $O_t$ by Griffin-Lim algorithm [@griffin1984signal] for comparison.

The spectrogram inpainting model architecture is based on state-of-the-art image inpainting model [@yu2018free] (see Fig. \[fig:model\_architecture\] (b2)). However, unlike natural images where x and y dimensions have similar scale and meaning, the time and frequency dimension in spectrograms have a significant difference. Therefore, we explore different components to deal with convolutions on spectrogram (see Fig. \[fig:model\_architecture\]).

Waveform Inpainting Model
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Our waveform inpainting models directly takes masked raw waveform as input and generate recovered waveforms as outputs. However, different from spectrograms, the raw waveforms are in much higher dimension ($>$16k/sec). If we have a one-second audio clip at a sample rate of 16 kHz, over 61 samples are needed to capture a single cycle of the 