Editorial for the Special Issue “Signal and Image Processing: From Theory to Applications” (1st Edition)

In an era defined by data-driven solutions, signal and image processing have emerged as cornerstones of technological innovation. From the theoretical frameworks that govern digital signal transformations to the practical applications reshaping industries, the field continues to evolve at an unprecedented pace. This Special Issue, titled “Signal and Image Processing: From Theory to Applications”, aims to bridge the gap between fundamental research and real-world implementation, highlighting the transformative impact of this discipline.

Signal and image processing rely on both rigorous mathematical bases [1,2,3] and model-from-data paradigms typical of artificial intelligence (AI) [4]. The theory, together with the more heuristic approach of AI, enables the efficient manipulation and extraction of information from raw data, leading to breakthroughs in fields such as medical imaging, telecommunications, or remote sensing. Advances in computational algorithms, machine learning, and AI further enhance the capabilities of traditional signal processing techniques, expanding their scope and efficiency. However, the trade-off for this rapid progress is in the lack of a comprehensive theory capable to “deterministically” explain the reasons of certain unexpected (in the positive sense) results.

This lack of a clear theoretical foundation has led to a split in the scientific community into two groups with different opinions: amazed by the AI results and, at the same time, concerned by the missing of a strong theoretical basis. For example, consider the ethical issues related to AI in self-driving cars.

What is collected in this Special Issue is a set of papers which could find difficulties to be classified in strict research frames and whose aim is to overlap the approach of these opposite feelings: mathematical theory-based models and from-data learning ones. Eleven manuscripts were accepted for publication in this Special Issue. Following an ideal sequence of a different “shade of theory”, the set of papers within it starts from a more theoretical formalization, continuing onto papers that interplay with applications, and finally arriving at works focused on these applications.

The contributions are listed below:

• Boccuto, A.; Gerace, I.; Giorgetti, V. A Graduated Non-Convexity Technique for Dealing Large Point Spread Functions. Appl. Sci. 2023, 13, 5861. https://doi.org/10.3390/app13105861.
• Chen, X.; Tan, Z.; Zhao, N.; Wang, J.; Liu, Y.; Tang, Y.; He, P.; Li, W.; Sun, J.; Si, J.; et al. Suitable Integral Sampling for Bandpass-Sampling Time-Modulated Fourier Transform Spectroscopy. Appl. Sci. 2024, 14, 1009. https://doi.org/10.3390/app14031009.
• de la Vega, J.; Riba, J.-R.; Ortega-Redondo, J.A. Mathematical Modeling of Battery Degradation Based on Direct Measurements and Signal Processing Methods. Appl. Sci. 2023, 13, 4938. https://doi.org/10.3390/app13084938.
• Li, H.; Tang, J.; Zhou, H. Hyperspectral Anomaly Detection Based on Multi-Feature Joint Trilateral Filtering and Cooperative Representation. Appl. Sci. 2023, 13, 6943. https://doi.org/10.3390/app13126943.
• Liu, S.; Li, Y.; Li, H.; Wang, B.; Wu, Y.; Zhang, Z. Visual Image Dehazing Using Polarimetric Atmospheric Light Estimation. Appl. Sci. 2023, 13, 10909. https://doi.org/10.3390/app131910909.
• Ricolfe-Viala, C.; Correcher, A.; Blanes, C. Detection of Bad Stapled Nails in Wooden Packages. Appl. Sci. 2023, 13, 5644. https://doi.org/10.3390/app13095644.
• Seracini, M.; Brown, S.R. Inpainting in Discrete Sobolev Spaces: Structural Information for Uncertainty Reduction. Appl. Sci. 2023, 13, 9405. https://doi.org/10.3390/app13169405.
• Seracini, M.; Vinti, G. Sampling by Difference as a Method of Applying the Sampling Kantorovich Model in Digital Image Processing. Appl. Sci. 2023, 13, 5594. https://doi.org/10.3390/app13095594.
• Tao, H.; Paul, A.; Wu, Z. Infrared Image Detection and Recognition of Substation Electrical Equipment Based on Improved YOLOv8. Appl. Sci. 2025, 15, 328. https://doi.org/10.3390/app15010328.
• Yao, Y.; Xu, X.; Jiang, Z. A New Chaotic Color Image Encryption Algorithm Based on Memristor Model and Random Hybrid Transforms. Appl. Sci. 2025, 15, 913. https://doi.org/10.3390/app15020913.
• Zhang, X.; Yang, Z.; Zhang, M.; Yu, Y.; Zhou, M.; Zhang, Y. Quantitative Monitoring Method for Conveyor Belt Deviation Status Based on Attention Guidance. Appl. Sci. 2024, 14, 6916. https://doi.org/10.3390/app14166916.

Despite remarkable advancements, challenges persist. High computational costs, real-time processing demands, and data privacy concerns pose significant hurdles. Furthermore, as artificial intelligence continues to integrate with signal processing, ethical considerations around bias and transparency must be addressed.

The future of signal and image processing lies in interdisciplinary collaboration, leveraging advancements in the mathematical theory. By merging theoretical rigor with application-driven research, the field will continue to shape the technological landscape in profound ways. By fostering a dialogue between theory and application, we hope to inspire new research directions and practical innovations that will redefine the possibilities of this dynamic field.