Numerical Approach for Improved Median Filter

G. K. H. Thondilege
G. H. J. Lanel
R. G. N. Meegama

image filtering, salt and pepper noise, gauss seidel, iterative methods, numerical
techniques

18 th February 2022

Image filtering can be identified as the most important and the very first stage of image
processing as usually captured images are degraded with several kinds of noises that lead to
reduced image quality. Therefore, highquality denoising techniques are needed to remove the
random noise while preserving the edges of the original image. The random noise that occurred in
images due to the error in the communication channel can be identified as the impulsive or salt-
and-pepper noise. In this case, the Median Filter (MF) is acting as a nonlinear process of removing
the impulsive or saltand- pepper noise. The MF commonly in use is a non-iterative technique and it
is based on an element-wise operator using a selected structural element. The concept of using
already approximated data for future value approximation is identified as a high convergence
technique in numerical analysis. In this paper, the mathematical concept behind the MF is
examined, and two iterative methods were developed row-wise and column-wise using the Gauss-
Seidel (GS) method, and a clear comparison is presented between the benchmark results obtained
by the conventional non-iterative MF and the results obtained for both improved iterative schemes
for the Darmstadt Noise Dataset (DND), Lena and Cameramen images using Mean Square Error
(MSE) values for different noise density values and compared the Peak Signal to Noise Ratio (PSNR)
results for Lena image with the results of [5] and [2]. Depending on the findings of the research
both the proposed Improved Median Filters (IMF) are giving denoised images with fewer MSE
values than that for the conventional MF and the column-wise IMF is more successful than the row-
wise IMF.