Introduction - Sparse Representations and Compressive Sensing for Imaging and Vision - page 1

Chapter 1
Introduction
Compressive sampling 1 [23, 47] is an emerging field that has attracted considerable
interest in signal/image processing, computer vision and information theory. Recent
advances in compressive sensing have led to the development of imaging devices
that sense at measurement rates below than the Nyquist rate. Compressive sensing
exploits the property that the sensed signal is often sparse in some transform
domain in order to recover it from a small number of linear, random, multiplexed
measurements. Robust signal recovery is possible from a number of measurements
that is proportional to the sparsity level of the signal, as opposed to its ambient
dimensionality.
While there has been remarkable progress in compressive sensing for static
signals such as images, its application to sensing temporal sequences such as videos
has also recently gained a lot of traction. Compressive sensing of videos makes a
compelling application towards dramatically reducing sensing costs. This manifests
itself in many ways including alleviating the data deluge problems [7] faced in
the processing and storage of videos. Using novel sensors based on this theory,
there is hope to accomplish tasks such as target tracking and object recognition
while collecting significantly less data than traditional systems.
In this monograph, we will present an overview of the theories of sparse
representation and compressive sampling and examine several interesting imaging
modalities based on these theories. We will also explore the use of linear and
non-linear kernel sparse representation as well as compressive sensing in many
computer vision problems including target tracking, background subtraction and
object recognition.
Writing this monograph presented a great challenge. Due to page limitations, we
could not include all that we wished. We beg the forgiveness of many of our fellow
researchers who have made significant contributions to the problems covered in this
monograph and whose works could not be discussed.
1 Also known as compressive sensing or compressed sensing.