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Adaptive Nonlinear Filters for Noise Removal

Adaptive Nonlinear Filters for Noise Removal

Presentation of the Adaptive Filters

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. Three adaptive nonlinear order statistics filters for noise removal are:

  • Adaptive LMS L Filter: the output is defined by the linear combination of the order statistics of the input samples in the filter window

    L filter Output

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

  • Adaptive LMS Ll Filter: it is an extension of the adaptive LMS L filter in that it preserves both space or time and order information. This is achieved by proper modification of the ordered input vector. Its output is calculated by use of the equation
    Ll filter Output

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

  • Modified Signal Adaptive (SAM) Median Filter: they 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:
    Ll filter Output

    According to the method of window adaptation employed, the modified signal adaptive median filter is further distinguished to the:

    • Symmetrical Signal Adaptive Median Filter: the window size is adapted in a symmetrical way
    • Morphological Signal Adaptive Median Filter: assymetrical window increment/decrement is performed

Performance Results

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

Noise Model

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

Table of Results

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

  • The adaptive Ll filter exhibits better performance results, for medium corrupted images, while the SAM filters are better in high corruption cases.
  • Considering the subjective criterion of perceived image quality of the processed image, the SAM filters perform better.
Original Image
Noisy Image
Adaptive LMS L Noise Removal
Adaptive LMS LI Noise Removal
Symmetrical SAM Noise Removal
Morphological SAM Adaptive LMS LI Noise Removal



Relevant Publications

S. Tsekeridou, C. Kotropoulos and I. Pitas, "Adaptive Order Statistic Filters for the Removal of Noise from Corrupted Images", SPIE Optical Engineering, vol. 37, no. 10, pp. 2798-2816, October, 1998.

C. Kotropoulos and I. Pitas, "Adaptive LMS L-filters for Noise Suppression in Images", IEEE Transactions on Image Processing, vol. 5, no. 12, pp. 1596-1609, December, 1996.

S. Tsekeridou, C. Kotropoulos and I. Pitas, "Morphological Signal Adaptive Median Filter for Noise Removal", in Proc. of 1996 Int. Conf. on Electronics, Circuits and Systems (ICECS'96), vol. 1, pp. 191-194, Rodos, Greece, 13-16 October, 1996.

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