A usual problem which arises in many image processing applications is the corruption of images by different kinds of noise, which leads to the degradation of their perceived quality. To deal with this problem, researchers in the field of image processing and analysis, have developed, over the years, various filtering algorithms for noise removal. The purpose of this Web Page is to present three adaptive nonlinear order statistics filters for noise removal, namely the:

- Adaptive
*LMS L*Filter - Adaptive
*LMS Ll*Filter - Modified
*Signal Adaptive (SAM) Median*Filter

According to the method of window adaptation employed, the modified signal adaptive median filter is further distinguished to the:*Symmetrical*Signal Adaptive Median Filter*Morphological*Signal Adaptive Median Filter

The **adaptive LMS L filter's** output is defined by the
linear combination of the order statistics of the input samples in the filter window:

The coefficient vector **a***(k)* is adapted at each step *k* accordingly
to the *LMS* adaptation algorithm.

The **adaptive LMS Ll filter** is an extension of the
adaptive

For the adaptation of its coefficient vector **c***(k)*, the *LMS*
algorithm is considered here as well.

The **modified SAM filters** adapt their behaviour in
accordance with the local signal to noise ratio. Thus, they behave differently in
homogeneous regions or edge regions. Their output is given by:

The difference between the symmetrical and the morphological *SAM* filters lies
only in the local window adaptation method, that they employ. The former adapts the window
size in a symmetrical way, while the latter performs assymetrical window
increment/decrement.

For the comparison of the performance of the proposed filters, a reference image called: Airfield, has been corrupted by the contaminated gaussian noise model:

The performance results in respect with *SNR, PSNR, MAE* and *MSE* measured
on the processed versions of a noisy image (Airm0s9l02), by the adaptive *L*, by the adaptive *Ll*,
by the symmetrical *SAM* and by the
morphological *SAM* filters, are concentrated in the following table:

The observation of both performance results and processed images leads to the following conclusions:

- The
**adaptive**exhibits better performance results, for medium corrupted images, while the*Ll*filterare better in high corruption cases.*SAM*filters - Considering the subjective criterion of perceived image quality of the processed image,
the
perform better.*SAM*filters

$Date: 1996/03/01 17:43:38 $

Sofia Tsekeridou <sofia@zeus.csd.auth.gr>