Title :
Optimum sampling vectors for Wiener filter noise reduction
Author :
Yamashita, Yukihiko
Author_Institution :
Dept. of Int. Dev. Eng., Tokyo Inst. of Technol., Japan
fDate :
1/1/2002 12:00:00 AM
Abstract :
Sampling is a very important and basic technique for signal processing. In the case that noise is added to a signal in the sampling process, we may use a reconstruction and noise reduction filter such as the Wiener filter. The Wiener filter provides a restored signal of which the mean square error is minimized. However, the mean square error by the Wiener filter depends on the sampling vectors. We may have the freedom to construct sampling vectors. We provide optimum sampling vectors under the condition that the Wiener filter is used for noise reduction for two cases wherein the noise is added before/after sampling. The sampling vectors provided in this paper may not be practical since they are very complicated. However, the minimum mean square error, which we provide theoretically, can be used for evaluating other sampling vectors. We provide all proofs of the theorems and lemmas. Furthermore, by experimental results, we show their advantages
Keywords :
Karhunen-Loeve transforms; Wiener filters; filtering theory; least mean squares methods; noise; optimisation; signal sampling; Karhunen-Loeve transform; MMSE; Wiener filter noise reduction; minimum mean square error; noise reduction filter; optimum sampling vectors; relative Karhunen-Loeve transform; signal processing; signal restoration; Data compression; Karhunen-Loeve transforms; Mean square error methods; Noise reduction; Pattern recognition; Sampling methods; Signal processing; Signal restoration; Signal sampling; Wiener filter;
Journal_Title :
Signal Processing, IEEE Transactions on