The objectives of IEEE Signal Processing Magazine ( SPM ) are to propose, for any IEEE Signal Processing Society (SPS) member and beyond, a wide range of tutorial articles on both methods and applications in signal and image processing. The articles are divided into different categories: feature articles, column and forum articles, and articles in special issues, the specificities of which are detailed on the SPM webpage “Information for Authors - SPM”.

Deep learning (DL) has been wildly successful in practice, and most of the state-of-the-art machine learning methods are based on neural networks (NNs). Lacking, however, is a rigorous mathematical theory that adequately explains the amazing performance of deep NNs (DNNs). In this article, we present a relatively new mathematical framework that provides the beginning of a deeper understanding of DL. This framework precisely characterizes the functional properties of NNs that are trained to fit to data. The key mathematical tools that support this framework include transform-domain sparse regularization, the Radon transform of computed tomography, and approximation theory, which are all techniques deeply rooted in signal processing.

As we gear up for the International Conference on Acoustics, Speech, and Signal Processing (ICASSP) 2024, it is essential to take a moment to celebrate the achievements and highlights of ICASSP 2023, which took place on Rhodes Island, Greece, this past June. ICASSP 2023 was a momentous event as it marked the first postpandemic ICASSP, and the return to in-person meetings. With the theme “Signal Processing in the AI Era,” the conference underscored the strong connection between signal processing and machine learning, highlighting the pivotal role of signal processing in shaping the development of artificial intelligence (AI).

Quaternions are still largely misunderstood and often considered an “exotic” signal representation without much practical utility despite the fact that they have been around the signal and image processing community for more than 30 years now. The main aim of this article is to counter this misconception and to demystify the use of quaternion algebra for solving problems in signal and image processing. To this end, we propose a comprehensive and objective overview of the key aspects of quaternion representations, models, and methods and illustrate our journey through the literature with flagship applications. We conclude this work by an outlook on the remaining challenges and open problems in quaternion signal and image processing.

Audio signal processing has passed many landmarks in its development as a research topic. Many are well known, such as the development of the phonograph in the second half of the 19th century and technology associated with digital telephony that burgeoned in the late 20th century and is still a hot topic in multiple guises. Interestingly, the development of audio technology has been fueled not only by advancements in the capabilities of technology but also by high consumer expectations and customer engagement.