The name is absent

21

bound on the noise magnitude, and σ(x) is the t<₂. error incurred by approximating
x using its largest к terms. This optimization can be solved using standard convex
programming algorithms.

For a more thorough review of CS and its application to imaging, see the article
by Duarte et al. [10].

2.2.2 CS imaging applications

Major applications of CS to imaging have included tomography [9], the optical single-
pixel camera [10,60], hyper-spectral imaging [61], digital holography [62], geophysical
imaging [63,64], and medical imaging such as magnetic resonance imaging (MRI) [65]
and photo-acoustic imaging [66].

In its wide range of applications to imaging, the CS theory has inspired new
imaging system designs which feature simpler hardware, and/or acquistion schemes
which feature better imaging efficiency. For instance, applying CS to MRI improves
the spatial resolution of MRI images limited by MRI scanning hardware, and allows
better image reconstruction from reduced sampling, thus accelerating acquisition for
patient comfort [65]. Both the optical single-pixel camera [10,60] and the single-pixel
THz imaging system in Chapter 4 use a single-pixel detector instead of a conventional
CCD array for imaging in visible light. In both cases, CS enables the implementation
of an imaging system with simpler and less expensive hardware, i.e., the single-pixel
detector.

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