Oversampled filter banks perform simultaneously subband decomposition and redundancy introduction. This redundancy has been shown to be useful to combat channel impairments, when the subbands are transmitted over a wireless channel, as well as quantization noise. This paper describes an implementation of the maximum \emph{a posteriori} and the minimum mean-square error (MMSE) estimators of the input signal from the noisy quantized subbands obtained at the output of some transmission channel. The relations between the input samples and the noisy subband samples are described using a factor graph. Belief propagation is then applied to get the posterior marginals of the input samples. The experimental results show that when the channel is clear, a linear MMSE estimate is satisfying. But, the proposed approaches perform significantly better than a reconstruction using the linear MMSE estimator when the channel is noisy: a gain in terms of channel SNR of more than $2$~dB is observed.