An Edge-Preserving Hybrid Filter Based on UFIR Filters for Reducing Gaussian Noise in Digital Images

In this paper, we propose a new digital filtering approach based on the FIR-Median Hybrid (FMH) structure, which incorporates an Unbiased Finite Impulse Response (UFIR) filter as its core component. The proposed filter employs spatially symmetric window configurations to reduce Gaussian noise while preserving edges in images. Although the scientific community is rapidly adopting machine-learning- and deep-learning-based filters, there are several reasons to continue developing filters based on traditional methods. For example, these methods are well understood and rely on a strong mathematical foundation. Moreover, the structure of the proposed filter is simple; thus, this type of filter may be appealing to engineers unfamiliar with the machine-learning field. The performance of the proposed filter was assessed using two datasets: the first consisted of a set of artificial binary images, and the second comprised a subset of the BOWS image dataset. We conducted three main experiments. In the first experiment, we fine-tuned the filter considering three window-shape configurations. In the second experiment, Gaussian noise was added to the images, and the proposed filter was compared against other filters using edge-preservation-oriented metrics such as the Structural Similarity Index Measure (SSIM), the Normalized Step Edge Response (NSER), and the Gradient Conduction Mean Square Error (GcMSE), among others. The third experiment evaluated the performance of the best-performing window-shape configurations. This final test was assessed quantitatively using the Friedman test to identify the best-performing structure, whereas qualitative assessment was conducted using a Mean Opinion Score (MOS) test. The results show that the proposed filter achieved improved performance according to the PSNR, SNR, RMSE, and GcMSE metrics. These findings suggest that the proposed filter can be used in practical applications such as image enhancement, computer vision, and edge-detection-based preprocessing.