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Summary: In this article, the asymptotic synchronization of a class of fuzzy inertial neural networks (FINNs) with time‐varying delays is investigated. First, the direct analysis approach is applied to replace the accustomed variable transformation and the reduced‐order method for addressing the inertial term. Second, a suitable Lyapunov function and control scheme are devised to obtain several new sufficient conditions to guarantee the asymptotic synchronization of the class of FINNs with time‐varying delays. It turns out that the obtained criteria are simpler and more effective. Meanwhile, some numerical examples demonstrate the effectiveness of the proposed strategies and verify the theoretical results. [ABSTRACT FROM AUTHOR]

Ultrasound imaging is widely used in medical diagnostics due to its non-invasive and real-time capabilities. However, existing methods often overlook the benefits of fractional-order filters for denoising and dehazing. Thus, this work introduces an efficient multi-scale wavelet method for dehazing and denoising ultrasound images using a fractional-order filter, which integrates a guided filter, directional filter, fractional-order filter, and haze removal to the different resolution images generated by a multi-scale wavelet. In the directional filter stage, an eigen-analysis of each pixel is conducted to extract structural features, which are then classified into edges for targeted filtering. The guided filter subsequently reduces speckle noise in homogeneous anatomical regions. The fractional-order filter allows the algorithm to effectively denoise while improving edge definition, irrespective of the edge size. Haze removal can effectively eliminate the haze caused by attenuation. Our method achieved significant improvements, with PSNR reaching 31.25 and SSIM 0.905 on our ultrasound dataset, outperforming other methods. Additionally, on external datasets like McMaster and Kodak24, it achieved the highest PSNR (29.68, 28.62) and SSIM (0.858, 0.803). Clinical evaluations by four radiologists confirmed its superiority in liver and carotid artery images. Overall, our approach outperforms existing speckle reduction and structural preservation techniques, making it highly suitable for clinical ultrasound imaging. [ABSTRACT FROM AUTHOR]