Hi, several algorithms for Audio dequantization based on signal sparsity have been proposed in the paper "Audio Dequantization Using (Co)Sparse (Non)Convex Methods". The MATLAB source codes are freely available on Github: https://github.com/zawi01/audio_dequantization
Even though the quantization scheme used in the paper is slightly different (standard Mid-riser quantizer), the codes can be easily edited (especially the projection functions) to work for arbitrary quantization scheme, assuming that quantization levels are known.