Thresholding-based sampling and signal reconstruction from multiple noisy observations

The problem of sampling and recovering bandlimited signals in the presence of noise is studied. A new signal acquisition technique, which collects multiple sets of thresholded signal's samples acquired at the Nyquist sampling rate, is proposed. The exact formula for mean integrated squared error of the proposed scheme is established. The obtained results show that the proposed technique gives better reconstruction accuracy than the common method using oversampling and post-filtering. Moreover, in most cases, the proposed scheme reduces the amount of data required for representation and reconstruction of signal. As a result, it provides the reduced data storage.