Using Statistical Non-Linear Filters for Gaussian Carina Nebula Image Denoising

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Noise affects images by distorting the features or reducing the required information. Gaussian noise is one of many types of noise that are characterized by normal distribution's statistical properties. Removing or reducing this noise is an essential step in image processing. James Webb Space Telescope (JWST) is a crucial tool for advancing our understanding of the universe across various domains. The images taken by the (JWST) are not only scientifically valuable for advancing our understanding but also have the potential to captivate and inspire people around the world. In this paper, we introduce several nonlinear filters, including Non-Local Mean (NLM) which gives weights to the pixels based on the distance from the noisy pixel. A Bilateral filter that gives weights for each pixel and then calculates the weighted distance. Propose a nonlinear filter depends on obtaining an appropriate smoothing parameter for the image by using the plug-in method and using it to estimate the image's density function, then using an appropriate noise reduction method on the estimated density function to extract the denoised image by removing the Gaussian noise from the Carina Nebula Image, the first image taken by (JWST) on 12 July 2022. The importance of this image lies in its potential to advance scientific knowledge, showcase technological prowess, inspire the public, and contribute to the broader mission of exploring and understanding the cosmos, Also, since it is the farthest point in the universe that humanity has been able to reach or take pictures of, it is therefore essential to preserve its quality to study all its elements or details. These nonlinear filters were therefore selected to highlight the significance of selecting the right technique that can handle, process, and preserve as many details as possible. They also elucidate the degree of advancement achieved in denoising and the distinction between the classical filters and the more sophisticated ones that have evolved to handle finer details. These filters consider the similarities and distances between the central pixel and its neighbours, they preserve the edges of the image as advanced features. Based on quality measurements Peak Signal to Noise Ratio (PSNR) and Structural similarity index measure (SSIM), the filter results were compared and show that the proposed filter gives high performance in restoring images under different Gaussian noise densities. Where it gives values of (42.51) and (0.99) for (PSNR) and (SSIM) respectively, then the bilateral filter gives (30.65) and (0.93) respectively.