High-Dimensional Data Analysis with Low-Dimensional Models Principles, Computation, and Applications

This book is about modeling and exploiting simple structure in signals, images, and data. In this chapter, we take our first steps in this direction. We study a class of models known as sparse models, in which the signal of interest is a superposition of a few basic signals (called “atoms”) selected from a large “dictionary.” This basic model arises in a surprisingly large number of applications. It also illustrates fundamental tradeoffs in modeling and computation that will recur throughout the book.