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).

Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, and medical imaging to dimensionality reduction and adaptive filtering. Many modern high-dimensional data and interactions thereof can be modeled as lying approximately in a low-dimensional subspace or manifold, possibly with additional structures, and its proper exploitations lead to significant cost reduction in sensing, computation, and storage.

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. 

Drilling is the riskiest activity in the oil-field exploration and development stage. Real-time measurements are needed to monitor drilling conditions to keep it in the safe operating envelope, guide the drilling system into the most productive zones, and provide information for further stages in the completion of the well. In this article, we describe digital communication systems for drilling, including data transmission and data compression. We begin by describing data transmission techniques used for two systems: mud-pulse telemetry (MPT) and electromagnetic (EM) telemetry.

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.

Semantic segmentation is the task of labeling every pixel in an image with a predefined object category. It has numerous applications in scenarios where the detailed understanding of an image is required, such as in autonomous vehicles and medical diagnosis. This problem has traditionally been solved with probabilistic models known as conditional random fields (CRFs) due to their ability to model the relationships between the pixels being predicted.

Traditionally, analytical methods have been used to solve imaging problems such as image restoration, inpainting, and superresolution (SR). In recent years, the fields of machine and deep learning have gained a lot of momentum in solving such imaging problems, often surpassing the performance provided by analytical approaches.