Hypercomplex signal and image processing extends upon conventional methods by using hypercomplex numbers in a unified framework for algebra and geometry. The special issue is divided into two parts and is focused on current advances and applications in computational signal and image processing in the hypercomplex domain.

It is our great pleasure to introduce the first part of this special issue to you! The IEEE Signal Processing Society (SPS) has completed 75 years of remarkable service to the signal processing community. When the Society was founded in 1948, we couldn’t imagine, for instance, how wireless networks of smartphones would be able to connect us easily at all times, or that an image processing algorithm would be able to detect cancer in a few seconds.

Thanks to the tremendous interest from the research community, the focus of the March issue of the IEEE Signal Processing Magazine is on the second volume of the special issue on physics-driven machine learning for computational imaging, which brings together nine articles of the 19 accepted papers from the original 47 submissions.

Recent years have witnessed a rapidly growing interest in next-generation imaging systems and their combination with machine learning. While model-based imaging schemes that incorporate physics-based forward models, noise models, and image priors laid the foundation in the emerging field of computational sensing and imaging, recent advances in machine learning, from large-scale optimization to building deep neural networks, are increasingly being applied in modern computational imaging.

The articles in this special section focus on nonconvex optimization for signal processing and machine learning. Optimization is now widely recognized as an indispensable tool in signal processing (SP) and machine learning (ML). Indeed, many of the advances in these fields rely crucially on the formulation of suitable optimization models and deployment of efficient numerical optimization algorithms. In the early 2000s, there was a heavy focus on the use of convex optimization techniques to tackle SP and ML applications.