Introduction - Sparse Representations and Compressive Sensing for Imaging and Vision - page 2

1.1 Outline

We begin the monograph with a brief discussion on compressive sampling in Sect. 2.
In particular, we present some fundamental premises underlying CS: sparsity,
incoherent sampling and non-linear recovery. Some of the main results are also
reviewed.
In Sect. 3, we describe several imaging modalities that make use of the theory
of compressive sampling. In particular, we present applications in medical imaging,
synthetic aperture radar imaging, millimeter wave imaging, single pixel camera and
light transport sensing.
In Sect. 4, we present some applications of compressive sampling in computer vi-
sion and image understanding. We show how sparse representation and compressive
sampling framework can be used to develop robust algorithms for target tracking.
We then present several applications in video compressive sampling. Finally, we
show how compressive sampling can be used to develop algorithms for recovering
shapes and images from gradients.
Section 5 discusses some applications of sparse representation and compressive
sampling in object recognition. In particular, we first present an overview of the
sparse representation framework. We then show how it can be used to develop robust
algorithms for object recognition. Through the use of Mercer kernels, we show
how the sparse representation framework can be made non-linear. We also discuss
multimodal multivariate sparse representation as well as its non-linear extension at
the end of this section.
In Sect. 6, we discuss recent advances in dictionary learning. In particular, we
present an overview of the method of optimal directions and the KSVD algorithms
for learning dictionaries. We then show how dictionaries can be designed to achieve
discrimination as well as reconstruction. Finally, we highlight some of the methods
for learning non-linear kernel dictionaries.
Finally, concluding remarks are presented in Sect. 7.