Audio super-resolution (ASR) aims to reconstruct the high-resolution signal from its corresponding low-resolution one, which is hard while the correlation between them is low.

In this paper, we propose a learning model, QISTA-Net-Audio, to solve ASR in a paradigm of linear inverse problem. QISTA-Net-Audio is composed of two components. First, an audio waveform can be presented as a complex-valued spectrum, which is composed of a real and an imaginary part, in the frequency domain. We treat the real and imaginary parts as an image, and predict a high-resolution spectrum but only keep the phase information from the viewpoint of image reconstruction. Second, we predict the magnitude information by solving the sparse signal reconstruction problem. By combining the predicted magnitude and the phase together, we can recover the high-resolution waveform. Comparison with the state-of-the-art method MfNet [1], in terms of measure metrics SNR, PESQ, and STOI, demonstrates the superior performance of our method.