ABSTRACT
Compressed or compressive sensing (CS) is a mathematical theory of measuring and retaining the most important part of the signal while sensing it. It effectively performs dimensionality reduction of a signal in a linear manner. It is one of the most exciting domains of modern times, and there is a deluge of papers and research outcomes available to the researcher. It has opened up new application vistas in the domains of computer science, electrical engineering, applied mathematics, remote sensing, medical imaging, communication, pattern recognition, and many more. Compressive sensing is an interdisciplinary field and draws its power from linear algebra, statistics and random processes, signal processing, optimization, communication theory, and space theory. This chapter is aimed at both the theorists and the practitioners. It will be a review for novice practitioners who would be interested in peeping through the domain, and also act as a quick reference to the theorist. This chapter will focus on the finite dimensional sparse signals and will provide an overview of the basic theory underlying the ideas of compressive sensing. Later in the chapter, we will discuss application based on the compressive sensing theory covered in the former part. We will develop a fragile domain watermarking application using CS. And finally, we present a further line of investigation in this domain: exploiting signal and measurement structure (i.e., use prior knowledge about the signal or physical process to be sensed for further reduction in the sampling rate). For more tangible discussions and simplicity, limited dimensional noncomplex signals are covered in this chapter.
