25
Figure 3.2 : Compressed sensing imaging results, (a) Magnitude of image recon-
structed by inverse Fourier transform using the full data set (4096 uniformly sampled
measurements), and (d) its phase. Note the phase distortion inherent in the THz beam
in (d). Compressed sensing reconstruction result using 500 measurements (12%) from
the full data set: (b) magnitude, and (e) phase. Compressed sensing with phase cor-
rection improves image quality and eliminates phase distortion (see (c) and (f)). All
figures show a zoom-in view on a 40 × 40 grid centered on the object.
and the measurement matrix Φ is M × N. Despite using fewer measurements, CS
can achieve perfect reconstruction of the object, assuming its sparsity, through an
optimization procedure [8]. Many optimization algorithms exist to solve this inverse
imaging problem. These algorithms aim to solve the minimization problem:
argmin ∣∣rr∣∣1 subject to constraint y = Фж, (3.1)
where ∣∣rr∣∣ι denotes the /!-norm [8]. Sometimes, when the original image x is
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