Theoretical understanding of the properties of smoothing depends upon the eigenstructure of the smoothing matrix. Hastie, Tibshirani, and Freidman (2001; The Elements of Statistical Learning, …

In other words, we have moved from estimating linear transformations of the features to ones, which we fit using a smoother (traditional packages use kernel smoothing, or spline smoothing, which is similar …

Gaussian Smoothing Filter Smoothing filter that does weighted averaging. The coefficients are a 2D Gaussian. Gives more weight at the central pixels and less weight to the neighbors. The farther away …

If nearby pixels have similar ”true”intensities, then we can use smoothing to reduce the noise. We can also think of smoothing as a simple example of how information can be passed between neighboring …

An issue with kernel smoothing (including running means) is that these methods have bad behavior at the edges of the plot. Observe what kernel smoothing does with perfectly regular, noiseless, linear data.

From this point of view the equations (6.1) are just a transparent reformulation of Fubini’s theorem, because by definition of T œ f (x + y)dμ(x)d∫(y) = Z f ±T d(μ£∫).

After the first pass the residuals are computed (called reroughing); the same smoothing sequence is applied to the residuals in a second pass, adding the result to the smooth of the first pass.