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Principal component analysis (PCA) is one of the most widely used dimension reduction techniques. A related easier problem is termed subspace learning or subspace estimation. Given relatively clean data, both are easily solved via singular value decomposition (SVD). The problem of subspace learning or PCA in the presence of outliers is called robust subspace learning (RSL) or robust PCA (RPCA).

With the proliferation of Internet of Things (IoT) applications, billions of household appliances, phones, smart devices, security systems, environment sensors, vehicles, buildings, and other radio-connected devices will transmit data and communicate with each other or people, and it will be possible to constantly measure and track virtually everything.

Sparse representation can efficiently model signals in different applications to facilitate processing. In this article, we will discuss various applications of sparse representation in wireless communications, with a focus on the most recent compressive sensing (CS)-enabled approaches.

Processing, storing, and communicating information that originates as an analog signal involves converting this information to bits. This conversion can be described by the combined effect of sampling and quantization, as shown in Figure 1. The digital representation is achieved by first sampling the analog signal to represent it by a set of discretetime samples and then quantizing these samples to a finite number of bits. 

Environmental monitoring is a topic of increasing interest, especially concerning the matter of natural hazards prediction. Regarding volcanic unrest, effective methodologies along with innovative and operational tools are needed to monitor, mitigate, and prevent risks related to volcanic hazards.