This thesis deals with audio dequantization from two differently quantized subband observations obtained using a wavelet filter bank. The input signal is decomposed by a single-level discrete wavelet transform into approximation and detail branches, which are decimated and then quantized using different bit depths. The aim of the thesis is to design and verify a reconstruction method that uses information from
both branches and reduces the distortion caused by quantization. The proposed approach is formulated as a convex optimization problem combining consistency conditions with the quantization intervals of both branches and a regularization term promoting sparsity of the signal in the time-frequency representation. This problem is solved using the Condat--Vũ algorithm, which allows efficient processing of several nonsmooth terms and projections onto feasible sets.

The method was implemented in MATLAB and tested on a database of monophonic recordings of musical instruments. The experiments were performed for different combinations of bit depths in the approximation and detail branches, for several types of Daubechies wavelet filters, and additionally for different depths of the wavelet decomposition. The reconstruction quality was evaluated using the objective metrics Signal-to-Distortion Ratio and Objective Difference Grade. The proposed method was compared with direct reconstruction using the inverse discrete wavelet transform and with a single-channel dequantization method based on the Chambolle--Pock algorithm. The results showed that the proposed method improves the reconstruction compared with direct reconstruction for most tested bit-depth combinations, especially according to the Signal-to-Distortion Ratio metric. With a suitable choice of bit depths in the approximation and detail branches, the method achieves better results than the single-channel reference dequantization at a comparable effective bit depth. Additional experiments showed that the db4 filter represents a compromise between reconstruction quality, simplicity, and processing stability. The results confirmed that subband signal processing combined with convex optimization is a usable approach for audio dequantization.