In this paper, having reviewed necessary preliminaries, including sparsity, Tsallis entropy, diversity, preprocessing, fisher information, and Cramer–Rao bound, we analyze the impact of preprocessing a signal on the signal sparsity related to Cramer–Rao lower bound and its main feature, for example, its reconstruction error. The main idea of this paper is to increase the sparsity of a vector, or to decrease its nonzero elements, then to compute the estimation error bound before and after sparsifying the signal. Finally, the claims are validated numerically. We implement Savitzky–Golay filtering on some ECG signals (applying MIT-BIH database of cardiac signals) and then compress them, to illustrate that the sparsity (the reconstruction error) of non-filtered signal was less (more) than that of filtered one. The results can be useful in signal compression and transmission procedures to have fewer recovery errors.
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Khorasani, S.M., Hodtani, G.A. & Kakhki, M.M. Decreasing Cramer–Rao lower bound by preprocessing steps. SIViP 14, 781–789 (2020). https://doi.org/10.1007/s11760-019-01605-2
- Gini index
- Estimator variance
- Cramer–Rao bound (CRB)
- Fisher information matrix (FIM)