The paper shows the potential of sparsity-based methods in restoring quantized signals. Following up on the study of Brauer et al. (IEEE ICASSP 2016), we significantly extend the range of the evaluation scenarios: we introduce the analysis (cosparse) model, we use more effective algorithms, we experiment with another time-frequency transform. The paper shows that the analysis-based model performs comparably to the synthesis-model, but the Gabor transform produces better results than the originally used cosine transform. Last but not least, we provide codes and data in a reproducible way.