Compressive Acquisition - Sparse Representations and Compressive Sensing for Imaging and Vision - page 16

Chapter 3
Compressive Acquisition

Many imaging modalities have been proposed that make use of the theory of
compressive sensing. In this chapter, we present several sensors designed using
CS theory. In particular, we focus on the Single Pixel Camera (SPC) [54], [149],
Magnetic Resonance Imaging (MRI) [79], [80], [108], Synthetic Aperture Radar
(SAR) imaging [103], passive millimeter wave imaging [104] and compressive light
transport sensing [110]. See [153] and [55] for excellent tutorials on the applications
of compressive sensing in the context of optical imaging as well as analog-to-
information conversion.

3.1 Single Pixel Camera

One of the first physical imagers that demonstrated the practicality of compressive
sensing in imaging was the Rice single pixel camera [54], [149]. The SPC essentially
measures the inner products between an N -pixel sampled version of the incident
light-field from the scene and a set of N -pixel test functions to capture the
compressive measurements. The SPC architecture is illustrated in Fig. 3.1 .
This architecture uses only a single detector element to image the scene. A digital
micromirror array is used to represent a pesudorandom binary array. The light-field
is then projected onto that array and the intensity of the projection is measured with
a single detector. The orientations of the mirrors in the micromirror array can be
changed rapidly, as a result a series of different pseudorandom projections can be
measured in relatively little time. The scene is then reconstructed from compressive
measurements using the existing CS reconstruction algorithms [54], [149].
Sample image reconstructions from SPC are shown in Fig. 3.2 . A black-and-
white picture of an ”R” is used to reconstruct using SPC. The original dimension
of the image is N

256. The reconstructed images using total variation
minimization from only 2% and 10% measurements are shown in the second and
third columns of Fig. 3.2 , respectively.

= 256 ×