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Single-channel Wiener filtering of deterministic signals in stochastic noise using the panorama

The Wiener filter is a well-known signal processing method for improving a noisy signal's quality. The Wiener filter requires either knowledge of or estimates of the power spectra of the signal-of-interest and of the undesired noise, leading to implementation challenges. In this paper, we show how a recently-developed second-order signal quantity termed the panorama can be employed to compute the Wiener filter for deterministic signals - containing nearly-constant frequency and phase components - in additive stochastic noise. We first show how the Wiener filter transfer function is related to the absolute value of the panorama and the power spectrum of the noisy measured signal. We then provide a practical procedure for estimating the absolute value of the panorama across frequency for single-channel sampled recordings. Numerical examples show the ability of the proposed procedure for estimating the panorama and for computing the Wiener filter for noisy deterministic signals.