Discrete LPA Accuracy

doi:10.1117/3.660178.ch5

Book: Local Approximation Techniques in Signal and Image Processing

Author(s): Vladimir Katkovnik, Karen Egiazarian, Jaakko Astola

Published: 2006

https://doi.org/10.1117/3.660178.ch5

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Abstract

The LPA accuracy is characterized by an error defined as the The analysis produced in the previous chapters concerns some aspects of the accuracy of the LPA operators. It has been proved that, as the sampling interval approaches zero, the discrete estimators can be replaced by corresponding integral ones. Further, it is shown that the kernels of these integral estimators are delta sequences. It immediately follows that, as hâ0 , the approximations of the signal as well as those of the derivatives become accurate. Both of these results jointly yield that there is a convergence of the LPA estimates to the true values of the signal and the derivatives. However, all of these results are mainly qualitative. In particular, in terms of the delta sequences, this convergence can be claimed only with respect to the test functions. Remember that the test function is continuous smooth with an infinite number of derivatives. In this chapter we analyze approximation errors of the LPA for more realistic classes of signals with the main goal of evaluating the order of errors as well as the convergence rate of the estimates. Together with the analysis with respect to the random noise, it gives a complete picture of the accuracy of the LPA estimators.