Mathematically Driven Identification and Generalizable Optimization of Smoothing Parameters for Speckle Noise...

Speckle noise, being multiplicative, degrades the quality of ultrasound images, making it very challenging to achieve successful diagnoses, particularly of PCOS, where ovarian cyst detection is crucial. Its nature, usually characterized by the Gamma distribution, makes it difficult to remove the noise without inducing distortion in the signal, resulting in loss of information and decreased diagnostic specificity. There is an inherent trade-off between the extent of noise suppression and the preservation of image details; therefore, this study aims to reduce speckle noise to the maximum extent possible while retaining critical diagnostic information. This paper proposes a novel framework to systematically determine and fine-tune the smoothing control parameters (SCPs) of five diagnostically important despeckling methods, particularly for ovarian ultrasound images. Experiments were performed on public and clinically acquired ovarian ultrasound datasets to evaluate the generalizability of the optimized SCPs. Among the applied speckle reduction techniques, the optimized Kuan filter with 512 NLOOKs yielded the best overall performance. It provided SSIM values between 0.91 and 1.00 ( $\pm 0.00$ -0.04), PSNR values between 74 and $79\text{dB}$ ( $\pm 1.94$ -2.68), and minimum MSE values of 0.00-0.01 ( $\pm 0.00$ ), indicating excellent speckle suppression and strong preservation of anatomical and textural information in ovarian ultrasound images. The Frost filter, tuned with a damping factor of 5, achieved comparably strong performance, maintaining an SSIM of $1.00\pm 0.00$ , PSNR values of 60- $67\text{dB}$ ( $\pm 1.00$ -2.66), and MSE values of 0.01-0.07 ( $\pm 0.00$ -0.04). These metrics highlight its ability to balance noise reduction with effective structural preservation. One-way ANOVA supported the superiority of these two filters, showing very high F-values and correspondingly low p-values, indicating highly significant performance differences ( $p<0.05$ ). Collectively, the optimized SCPs provide a reliable and generalizable strategy for improving ultrasound image quality across diverse datasets.