File:CMB Wiener filter example.png

English: This figure demonstrates the effect of a Wiener filter on a noisy simulated observation of the Cosmic Microwave Background (CMB). The input data ${\displaystyle d}$ is shown on the left, and is the sum of CMB, which is a Gaussian random field which is strongly correlated in real space (but diagonal in frequency space), and a noise field, which has independent values in each pixel, but increasing standard deviation towards the edge. The signal and noise have covariance ${\displaystyle S}$ and ${\displaystyle N}$ respectively.

The center panel shows the Wiener-filtered result, computed via ${\displaystyle {\hat {s}}=(S^{-1}+N^{-1})^{-1}N^{-1}d}$.

The right panel shows the true input signal.