Modified Wiener Filter using Scaled Median Absolute Deviation Normalized for Gaussian Noise Reduction

Modified versions of the Wiener filter that replace the mean with the median (MMWF) can better reduce Gaussian noise in images than the classical Wiener filter (WF). However, performance gradually decreases as the noise variance increases. To overcome these limitations, we propose a modified Wiener filter (MADNWF) that replaces the mean with the scaled median absolute deviation (MADN). Similar to MMWF, our modification to the Wiener filter uses a local kernel to average over each pixel. Instead of using the median alone, we replace it with MADN. We used four public datasets for the experiment: Set12, the Tampere17 noise-free dataset, TID2008, and the BSD68 dataset. The first step of this study was to generate 'degraded' images. To achieve this, we added a random amount of zero-mean Gaussian noise with noise variances ranging from 10 to 90, in increments of 10, to every image in the dataset. For comparison with the WF and MMWF, we then applied the proposed MADNWF to reduce noise in degraded images. We evaluated the resulting performance by comparing the reduced noise images with the original images using the Structural Similarity Index (SSIM) and Peak Signal-to-Noise Ratio (PSNR) metrics. Experimental results demonstrate that MADNWF consistently outperforms the other methods. At a low noise level (variance = 10), MMWF with a 3x3 filter slightly outperforms in fine-structural preservation, achieving a peak SSIM of 0.6676. However, as the noise intensity increases (variances from 20 to 90), MADNWF achieves complete dominance across all datasets. MADNWF achieves the highest PSNR, up to 33.27 dB at low noise levels, representing an improvement of up to 0.28 dB over WF. Under extreme noise conditions (variance = 90), the MADNWF 7x7 configuration achieves superior image cleanliness (up to 28.91 dB), whereas the MADNWF 5x5 setting serves as the optimal trade-off for structure preservation, outperforming MMWF with an SSIM margin increase of up to 0.0276. In conclusion, our results demonstrate that MADNWF helps reduce the noise distribution in natural images.