Edge-Aware Spatial Denoising Filtering Based on a Psychological Model of Stimulus Similarity

Noise reduction is a fundamental operation in image quality enhancement. In recent years, a large body of techniques at the crossroads of statistics and functional analysis have been developed to minimize the blurring artifact introduced in the denoising process. Recent studies focus on edge-aware filters due to their tendency to preserve image structures. In this paper, we adopt a psychological model of similarity based on Shepard's generalization law and introduce a new signal-dependent window selection technique. Such a focus is warranted, because blurring is essentially a cognitive act related to the human perception of physical stimuli (pixels). The proposed windowing technique can be used to implement a wide range of edge-aware spatial denoising filters, thereby transforming them into nonlocal filters. We employ simulations using both synthetic and real image samples to evaluate the performance of the proposed method by quantifying the enhancement in the signal strength, noise suppression, and structural preservation measured in terms of the peak signal-to-noise ratio (PSNR), mean square error (MSE), and structural similarity (SSIM) index, respectively. In our experiments, we observe that incorporating the proposed windowing technique in the design of mean, median, and nonlocal means filters substantially reduces the MSE while simultaneously increasing the PSNR and the SSIM.