SPM Articles

The flexibility and dexterity of human limbs rely on the processing of a vast quantity of signals within the sensory-motor networks in the brain and spinal cord, distilled into stimuli that govern the commands and movements. Hence, the use of assistive devices, such as robotic limbs or exoskeletons, is critically dependent on the processing of a large number of heterogeneous signals to mimic natural movements.

Deep learning, in general, focuses on training a neural network from large labeled datasets. Yet, in many cases, there is value in training a network just from the input at hand. This is particularly relevant in many signal and image processing problems where training data are scarce and diversity is large on the one hand, and on the other, there is a lot of structure in the data that can be exploited.

By “social learning,” in this article we refer to mechanisms for opinion formation and decision making over graphs and the study of how agents’ decisions evolve dynamically through interactions with neighbors and the environment. The study of social learning strategies is critical for at least two reasons.

As I take on the President of the Signal Processing Society (SPS) role, I am excited to connect with you through this column. I look forward to introducing myself and inviting you, the members, to join our volunteers in shaping our shared future.

Hypercomplex signal processing (HSP) provides state-of-the-art tools to handle multidimensional signals by harnessing the intrinsic correlation of the signal dimensions through Clifford algebra. Recently, the hypercomplex representation of the phase retrieval (PR) problem, wherein a complex-valued signal is estimated through its intensity-only projections, has attracted significant interest.

Vector-valued signals are crucial in science and engineering. The evolving field of hypercomplex signal processing, particularly quaternion algebra, offers a concise and natural approach to handling vectorial data. In multicomponent seismology, for instance, vector-valued signal processing finds a natural fit that has been exploited in several applications.

This article aims to identify core research directions and provide a comprehensive overview of major advancements in the field of hypercomplex signal and image processing techniques using network graph theory. The methodology employs community detection algorithms on research networks to uncover relationships among researchers and topic fields in the hypercomplex domain.

Novel computational signal and image analysis methodologies based on feature-rich mathematical/computational frameworks continue to push the limits of the technological envelope, thus providing optimized and efficient solutions. Hypercomplex signal and image processing is a fascinating field that extends conventional methods by using hypercomplex numbers in a unified framework for algebra and geometry. 

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.

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.