Biomedical Engineering Reference
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Fig. 4.10 A single raw lensfree hologram is compared against a super-resolved hologram, which
is the result of processing multiple raw and shifted holograms [ 19 ]. The sub-pixel shifts between
the different frames are shown on the right . The super-resolved hologram reveals more fringes and
resolves the aliasing apparent in the raw hologram. The additional fringes in the super-resolution
hologram translate to a higher spatial resolution image (after appropriate twin-image elimination
processing), as illustrated in the lower reconstructed images
After all the shifts of the lensfree raw holograms (each captured using an
individual LED within the source-array) are computed, the PSR algorithm can
be invoked. The goal of PSR is to find a single high-resolution hologram, which
recovers all the shifted low-resolution holograms once downsampled with the
appropriate shifts. A simple way to reach this desired hologram is to minimize the
following cost function:
Y fl
Y fl ;
X
1
2
˛
2
x k;i / 2
C.Y/
D
.x k;i Q
C
(4.3)
k D 1;:::;p
i
D
1;:::;M
Q
where x k are the measured holograms,
x k are the corresponding images which are
obtained from downsampling the high-resolution image Y , and the index iruns
over all pixels of a given hologram. The last term in Eq. 4.3 penalizes very high-
frequency components which could be artifacts of the optimization process, and the
strength of this penalty can be adjusted using the parameter ˛. The cost function of
Eq. 4.3 is a quadratic function of the pixels of the high-resolution images and can
therefore be straightforwardly minimized using, for example, the conjugate gradient
descent method.
An experimental demonstration of the resolution enhancement due to the mul-
tiframe PSR is shown in Fig. 4.10 . A single raw low-resolution hologram and its
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