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Lee's local statistics filter

The Lee filter [11] is able to smooth away noise in flat regions, but leave fine details (such as lines and text) unchanged. It uses small windows (3x3,5x5 or 7x7). Within each window, the local mean and variance are estimated:

In regions of no signal activity, the filter outputs the local mean ( ). When signal activity is detected, the filter passes the original signal through unchanged. This is achieved by filters of the form

where is the central pixel in the window. The parameter ranges between 0 (for flat regions) and 1 (for regions with high signal activity). For the additive noise case, this formula for is used:

where is an estimate of the noise variance.

  
Figure 1.4: Lee filter example

The Lee filter senses when it is being applied to a region which is constant in intensity, and responds by smoothing. In regions which contain signal activity (for example, lines and edges), the Lee filter shuts down its smoothing. The Lee filter can thus smooth in flat regions but still preserve sharp details. Its major drawback is that it leaves noise in the vicinity of edges and lines (Figure 1.4). Variants of this filter handle multiplicative noise and sharpening [11].



Todd Veldhuizen
Fri Jan 16 15:16:31 EST 1998