Biomedical Engineering Reference

In-Depth Information

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