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IEEE Signal Processing Magazine

The notion of graph filters can be used to define generative models for graph data. In fact, the data obtained from many examples of network dynamics may be viewed as the output of a graph filter. With this interpretation, classical signal processing tools, such as frequency analysis, have been successfully applied with analogous interpretation to graph data, generating new insights for data science. What follows is a user guide on a specific class of graph data, where the generating graph filters are low pass; i.e., the filter attenuates contents in the higher graph frequencies while retaining contents in the lower frequencies. Our choice is motivated by the prevalence of low-pass models in application domains such as social networks, financial markets, and power systems. 
The articles in this special section focus on graph signal processing. Generically, the networks that sustain our societies can be understood as complex systems formed by multiple nodes, where global network behavior arises from local interactions between connected nodes. More succinctly, a network or a graph can be defined as a structure that encodes relationships between pairs of elements of a set. The simplicity of this definition drives the application of graphs and networks to a wide variety of disciplines, such as biology, medicine, psychology, sociology, economics, engineering, computer science, and so on.
When we started to organize ICASSP in Barcelona, one of our goals was to promote an environmentally conscious conference by trying to reduce the use of paper, using recyclable plastic badges, replacing USB sticks with electronic downloads, and promoting the use of digital tools as an alternative to the conference booklet. Now that the conference is over, we can say that we promised a green ICASSP, and we certainly delivered! 
 
Phase retrieval (PR), also sometimes referred to as quadratic sensing, is a problem that occurs in numerous signal and image acquisition domains ranging from optics, X-ray crystallography, Fourier ptychography, subdiffraction imaging, and astronomy. In each of these domains, the physics of the acquisition system dictates that only the magnitude (intensity) of certain linear projections of the signal or image can be measured. Without any assumptions on the unknown signal, accurate recovery necessarily requires an overcomplete set of measurements.

Zeroth-order (ZO) optimization is a subset of gradient-free optimization that emerges in many signal processing and machine learning (ML) applications. It is used for solving optimization problems similarly to gradient-based methods. However, it does not require the gradient, using only function evaluations. Specifically, ZO optimization iteratively performs three major steps: gradient estimation, descent direction computation, and the solution update. In this article, we provide a comprehensive review of ZO optimization, with an emphasis on showing the underlying intuition, optimization principles, and recent advances in convergence analysis.

Optimization lies at the heart of machine learning (ML) and signal processing (SP). Contemporary approaches based on the stochastic gradient (SG) method are nonadaptive in the sense that their implementation employs prescribed parameter values that need to be tuned for each application. This article summarizes recent research and motivates future work on adaptive stochastic optimization methods, which have the potential to offer significant computational savings when training largescale systems.

Many contemporary applications in signal processing and machine learning give rise to structured nonconvex nonsmooth optimization problems that can often be tackled by simple iterative methods quite effectively. One of the keys to understanding such a phenomenon-and, in fact, a very difficult conundrum even for experts-lies in the study of "stationary points" of the problem in question. Unlike smooth optimization, for which the definition of a stationary point is rather standard, there are myriad definitions of stationarity in nonsmooth optimization.

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.

We continue to live through a unique experience in history. Out of concern for each other, we have voluntarily participated in essentially shutting down economic activities across the globe. We have discovered the interdependencies and precariousness of our lives and livelihoods. We have learned who and what is essential or important and have simplified our lives. We have realized the virtue of patience and self-kindness as we navigate the tremendous challenges of working from home and balancing our work obligations and family needs.

The safety and success of autonomous vehicles (AVs) depend on their ability to accurately map and respond to their surroundings in real time. One of the most promising recent technologies for depth mapping is single-photon lidar (SPL), which measures the time of flight of individual photons. The long-range capabilities (kilometers), excellent depth resolution (centimeters), and use of low-power (eye-safe) laser sources renders this modality a strong candidate for use in AVs. 

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