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Generalized Wiener Filter
The Wiener filter as originally proposed by Norbert Wiener is a signal processing filter which uses knowledge of the statistical properties of both the signal and the noise to reconstruct an optimal estimate of the signal from a noisy one-dimensional time-ordered data stream. The generalized Wiener filter generalizes the same idea beyond the domain of one-dimensional time-ordered signal processing, with two-dimensional image processing being the most common application. Description Consider a data vector d which is the sum of independent signal and noise vectors d = s+n with zero mean and covariances \langle ss^T\rangle=S and \langle nn^T\rangle=N. The generalized Wiener Filter is the linear operator G which minimizes the expected residual between the estimated signal and the true signal, e = \langle(Gd-s)^T(Gd-s)\rangle. The G that minimizes this is G = S(S+N)^, resulting in the Wiener estimator \hat s = S(S+N)^d. In the case of Gaussian distributed signal and noise, this estimat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wiener Filter
In signal processing, the Wiener filter is a filter used to produce an estimate of a desired or target random process by linear time-invariant ( LTI) filtering of an observed noisy process, assuming known stationary signal and noise spectra, and additive noise. The Wiener filter minimizes the mean square error between the estimated random process and the desired process. Description The goal of the Wiener filter is to compute a statistical estimate of an unknown signal using a related signal as an input and filtering that known signal to produce the estimate as an output. For example, the known signal might consist of an unknown signal of interest that has been corrupted by additive noise. The Wiener filter can be used to filter out the noise from the corrupted signal to provide an estimate of the underlying signal of interest. The Wiener filter is based on a statistical approach, and a more statistical account of the theory is given in the minimum mean square error (MMSE) e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
