27
Number of Measurements (M)
Figure 3.3 : Comparison of quality of image reconstruction between CS with and with-
out phase correction. As the number of measurements (M) used in CS increases, the
mean-squared error (MSE) between the magnitudes of the reconstructed image and
the reference image (see Fig 3.2(a)), normalized by the energy of the reference image,
decreases. CS with phase correction shows superior reconstruction performance.
an object with a constant phase profile has a more sparse representation in wavelet
basis than one with a spatially varying phase profile, CS reconstruction using phase
correction yields superior performance for a given number of measurements.
3.2.3 CS and phase retrieval
If the object mask in Figure 3.1 moves away from the object plane, the acquired
Fourier data will have the correct Fourier magnitude but a distorted phase. No longer
can one use the phase data for image reconstruction. However, an image can still
be reconstructed by combining CS with the well-known technique of phase retrieval
(PR) [67]. Moravec et al. recently developed a PR minimization algorithm, called
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