Low-complexity pixel detection for images with misalignment and interpixel interference in holographic data storage

Chi-Yun Chen; Chih-Cheng Fu; Tzi-Dar Chiueh

doi:10.1364/AO.47.006784

Applied Optics
Vol. 47,
Issue 36,
pp. 6784-6795
(2008)
•https://doi.org/10.1364/AO.47.006784

Low-complexity pixel detection for images with misalignment and interpixel interference in holographic data storage

Chi-Yun Chen, Chih-Cheng Fu, and Tzi-Dar Chiueh

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Chi-Yun Chen, Chih-Cheng Fu, and Tzi-Dar Chiueh, "Low-complexity pixel detection for images with misalignment and interpixel interference in holographic data storage," Appl. Opt. 47, 6784-6795 (2008)

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Abstract

This paper presents an efficient solution to recovering data pixels of images that have undergone optical and electrical channel impairments in holographic data storage systems. The channel impairments considered include interpixel interference, three types of misalignment, and noise. The proposed misalignment-compensation scheme, consisting of realignment and rate conversion, can effectively eliminate misalignment with more than 84% reduction in additions and 74% reduction in multiplications. In addition, several low-complexity techniques are introduced to reduce the complexity of a two-dimensional maximum a posteriori pixel detection method by up to 95% and do so with negligible degradation in detection performance.

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Parameters	Simulation Settings
Page Size	$512 \times 512$
$λ / f_{L} / Δ$	$515 nm / 89 mm / 18 μm$
$f f_{SLM} / f f_{CCD}$	$0.9 / 0.9$
ε	10
M	2
$(γ_{x}, γ_{y}, σ_{x}, σ_{y}, θ)$	(0.98, 0.98, 0.5, 0.5, $0.5 °$ )

Compensation Method	Implementation Scheme	Computational Complexity
		Additions/SLM Pixel	Multiplications/SLM Pixel
Ra	—	$K^{2}$	$K^{2}$
$Ra + Rc$	Direct $2 D + 2 D$	$K^{2} (M^{2} γ_{x} γ_{y}) + T_{x} T_{y}$	$K^{2} (M^{2} γ_{x} γ_{y}) + T_{x} T_{y}$
	Scheme 1 $1 D + 1 D$	$2 K (M^{2} γ_{x} γ_{y}) + T_{x} + T_{y}$	$2 K (M^{2} γ_{x} γ_{y}) + T_{x} + T_{y}$
	$Scheme 1 + Scheme 2$ 1D	$K (T_{x} + T_{y})$	$2 (K - 1) + (K + 1) (T_{x} + T_{y})$

$K = 6$ , $T_{x} = T_{y} = 2$	Addition		Multiplication
Realignment only	36	—	36	—
$Ra + Rc$ (Direct)	148	100%	148	100%
$Ra + Rc$ (Scheme 1)	52	35.14%	52	35.14%
$Ra + Rc$ (Schemes 1 and 2)	24	16.22%	38	25.68%

	$Q = 0$	$Q = 1$	$Q = 2$	$Q = 3$
Number of candidates	1	8	28	56
Average addition per candidate	3	1	1	1

$w = 0.8 @ 18 dB$	Addition	Multiplication
Direct Implementation	100%	100%
IR	57.7%	57.7%
$IR + CR$	6.28%	6.28%
$IR + CR + NR$	4.82%	4.82%
$IR + CR + NR + AR$	3.47%	4.82%

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Applied Optics