Structural Similarity Optimized Wiener Filter: A Way to Fight Image Noise

Wiener filter is widely used for image denoising and restoration. It is alternatively known as the minimum mean square error filter or the least square error filter, since the objective function used in Wiener filter is an age-old benchmark called the Mean Square Error (MSE). Wiener filter tries to approximate the degraded image so that its objective function is optimized. Although MSE is considered to be a robust measurement metric to assess the closeness between two images, recent studies show that MSE can sometimes be misleading whereas the Structural Similarity (SSIM) can be an acceptable alternative. In spite of having this misleading natured objective function, Wiener filter is being heavily used as a fundamental component in many image denoising and restoration algorithms such as in current state-of-the-art of image denoising-BM3D. In this study, we explored the problem with the objective function of Wiener filter. We then improved the Wiener filter by optimizing it for SSIM. Our proposed method is tested using the standard performance evaluation methods. Experimental results show that the proposed SSIM optimized Wiener filter can achieve significantly better denoising (and restoration) as compared to its original MSE optimized counterpart. Finally, we discussed the potentials of using our improved Wiener filter inside BM3D in order to eventually improve BM3D's denoising performance.