Retrieving quantized signal from its noisy version

In this paper we propose an algorithm to retrieve a quantized data from its noisy version. To find the optimum quantization levels, a multistage process minimizes the Mean Square Error (MSE) at each quantization level by using the Minimum Noiseless Description Length (MNDL) algorithm. Consequently, the procedure denoises and recovers the quantized data simultaneously. The prior knowledge that the original signal is a quantized data enables us to denoise the data more efficiently. We show that in high Signal to Noise Ratio (SNR) cases, the retrieved levels are the same as the original levels of the quantized signal. However, in low SNR cases, since the quantized signal has been highly effected by the additive noise, the optimum retrieved levels are less than the original quantization levels.