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SPM Articles

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.

Signal processing (SP) is a “hidden” technology that has transformed the digital world and changed our lives in so many ways. The field of digital SP (DSP) took off in the mid-1960s, aided by the integrated circuit and increasing availability of digital computers. Since then, the field of DSP has grown tremendously and fueled groundbreaking advances in technology across a wide range of fields with profound impact on society. 

When I began writing this 75th anniversary article celebrating women in signal processing (SP), I reread the 1998 editorial titled “Fifty Years of Signal Processing: 1948–1998” [1] . At that time, IEEE had more than 300,000 members in 150 nations, the world’s largest professional technical Society. Within the IEEE umbrella, there were 37 IEEE Societies and technical groups, and the IEEE Signal Processing Society (SPS) was the oldest among its many Societies.

Throughout the IEEE Signal Processing Society’s (SPS’s) history, conferences have functioned as a main way to connect within the Society, bringing together the signal processing research community to discuss and debate, establish research collaborations, and have a good time.

Humans can listen to a target speaker even in challenging acoustic conditions that have noise, reverberation, and interfering speakers. This phenomenon is known as the cocktail party effect . For decades, researchers have focused on approaching the listening ability of humans. One critical issue is handling interfering speakers because the target and nontarget speech signals share similar characteristics, complicating their discrimination. 

Visualizing information inside objects is an everlasting need to bridge the world from physics, chemistry, and biology to computation. Among all tomographic techniques, terahertz (THz) computational imaging has demonstrated its unique sensing features to digitalize multidimensional object information in a nondestructive, nonionizing, and noninvasive way.

Electromagnetic (EM) imaging is widely applied in sensing for security, biomedicine, geophysics, and various industries. It is an ill-posed inverse problem whose solution is usually computationally expensive. Machine learning (ML) techniques and especially deep learning (DL) show potential in fast and accurate imaging. However, the high performance of purely data-driven approaches relies on constructing a training set that is statistically consistent with practical scenarios, which is often not possible in EM-imaging tasks. Consequently, generalizability becomes a major concern.

The compressive sensing (CS) scheme exploits many fewer measurements than suggested by the Nyquist–Shannon sampling theorem to accurately reconstruct images, which has attracted considerable attention in the computational imaging community. While classic image CS schemes employ sparsity using analytical transforms or bases, the learning-based approaches have become increasingly popular in recent years. Such methods can effectively model the structure of image patches by optimizing their sparse representations or learning deep neural networks while preserving the known or modeled sensing process. 

In addition to the impressive predictive power of machine learning (ML) models, more recently, explanation methods have emerged that enable an interpretation of complex nonlinear learning models, such as deep neural networks. Gaining a better understanding is especially important, e.g., for safety-critical ML applications or medical diagnostics and so on. Although such explainable artificial intelligence (XAI) techniques have reached significant popularity for classifiers, thus far, little attention has been devoted to XAI for regression models (XAIR). 


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