In optics, Zernike polynomials are widely used in testing, wavefront sensing, and aberration theory. This unique set of radial polynomials is orthogonal over the unit circle and finite on its boundary. This Letter presents a recursive formula to compute Zernike radial polynomials using a relationship between radial polynomials and Chebyshev polynomials of the second kind. Unlike the previous algorithms, the derived recurrence relation depends neither on the degree nor on the azimuthal order of the radial polynomials. This leads to a reduction in the computational complexity.

Structural health monitoring (SHM) involves the control and analysis of mechanical systems to monitor the variation of geometric features of engineering structures. Damage processing is one of the issues that can be addressed by using several techniques derived from image processing. There are two types of SHM: contact-based and non-contact methods. Sensors, cameras, and accelerometers are examples of contact-based SHM, whereas photogrammetry, infrared thermography, and laser imaging are non-contact SHM techniques. In this research, our focus centres on image processing algorithms to identify the crack and analyze its properties to detect occurred damages. Based on the literature review, several preprocessing approaches were employed including image enhancement, image filtering to remove the noise and blur, and dynamic response measurement to predict the crack propagation.

Non-Invasive Inspection (NII) has become a fundamental tool in modern industrial maintenance strategies. Remote and online inspection features keep operators fully aware of the health of industrial assets whilst saving money, lives, production and the environment. This paper conducted crucial research to identify suitable sensing techniques for machine health diagnosis in an NII manner, mainly to detect machine shaft misalignment and gearbox tooth damage for different types of machines, even those installed in a hostile environment, using literature on several sensing tools and techniques. The researched tools are critically reviewed based on the published literature. However, in the absence of a formal definition of NII in the existing literature, we have categorised NII tools and methods into two distinct categories. Later, we describe the use of these tools as contact-based, such as vibration, alternative current (AC), voltage and flux analysis, and non-contact-based, such as laser, imaging, acoustic, thermographic and radar, under each category in detail. The unaddressed issues and challenges are discussed at the end of the paper. The conclusions suggest that one cannot single out an NII technique or method to perform health diagnostics for every machine efficiently. There are limitations with all of the reviewed tools and methods, but good results possible if the machine operational requirements and maintenance needs are considered. It has been noted that the sensors based on radar principles are particularly effective when monitoring assets, but further comprehensive research is required to explore the full potential of these sensors in the context of the NII of machine health. Hence it was identified that the radar sensing technique has excellent features, although it has not been comprehensively employed in machine health diagnosis.

The early detection of breast cancer is essential for improving treatment outcomes, and recent advancements in artificial intelligence (AI), combined with image processing techniques, have shown great potential in enhancing diagnostic accuracy. This study explores the effects of various image processing methods and AI models on the performance of early breast cancer diagnostic systems. By focusing on techniques such as Wiener filtering and total variation filtering, we aim to improve image quality and diagnostic precision. The novelty of this study lies in the comprehensive evaluation of these techniques across multiple medical imaging datasets, including a DCE-MRI dataset for breast-tumor image segmentation and classification (BreastDM) and the Breast Ultrasound Image (BUSI), Mammographic Image Analysis Society (MIAS), Breast Cancer Histopathological Image (BreakHis), and Digital Database for Screening Mammography (DDSM) datasets. The integration of advanced AI models, such as the vision transformer (ViT) and the U-KAN model—a U-Net structure combined with Kolmogorov–Arnold Networks (KANs)—is another key aspect, offering new insights into the efficacy of these approaches in different imaging contexts. Experiments revealed that Wiener filtering significantly improved image quality, achieving a peak signal-to-noise ratio (PSNR) of 23.06 dB and a structural similarity index measure (SSIM) of 0.79 using the BreastDM dataset and a PSNR of 20.09 dB with an SSIM of 0.35 using the BUSI dataset. When combined filtering techniques were applied, the results varied, with the MIAS dataset showing a decrease in SSIM and an increase in the mean squared error (MSE), while the BUSI dataset exhibited enhanced perceptual quality and structural preservation. The vision transformer (ViT) framework excelled in processing complex image data, particularly with the BreastDM and BUSI datasets. Notably, the Wiener filter using the BreastDM dataset resulted in an accuracy of 96.9% and a recall of 96.7%, while the combined filtering approach further enhanced these metrics to 99.3% accuracy and 98.3% recall. In the BUSI dataset, the Wiener filter achieved an accuracy of 98.0% and a specificity of 98.5%. Additionally, the U-KAN model demonstrated superior performance in breast cancer lesion segmentation, outperforming traditional models like U-Net and U-Net++ across datasets, with an accuracy of 93.3% and a sensitivity of 97.4% in the BUSI dataset. These findings highlight the importance of dataset-specific preprocessing techniques and the potential of advanced AI models like ViT and U-KAN to significantly improve the accuracy of early breast cancer diagnostics.