Filtering random noise from deterministic signals via data compression

摘要

We present a novel technique for the design of filters for random noise, leading to a class of filters called Occam filters. The essence of the technique is that when a lossy data compression algorithm is applied to a noisy signal with the allowed loss set equal to the noise strength, the loss and the noise tend to cancel rather than add. We give two illustrative applications of the technique to univariate signals. We also prove asymptotic convergence bounds on the effectiveness of Occam filters.