Color Filter Arrays: Representation, Analysis and A Design Methodology

We have developed a novel mathematical representation of CFAs, which makes analysis of all the CFAs easy, simple and visual, and based on that, a design methodology is developed for new CFAs. The comparison between the tentatively designed new CFAs and the Bayer CFA is exciting. The detailed results are listed below.

Color PSNR of the images demosaicked with 4 methods applied to Bayer CFA pattern and the new patterns

	Bayer				CFA4a		CFA4b		CFA6	CFA23
Image	Homo	POCS	Naive	Adapt	Naive	Adapt	Naive	Adapt	Naive	Naive
1	35.13	37.82	35.55	38.14	39.48	39.65	40.31	40.39	40.16	40.82
2	39.10	39.58	39.20	39.82	39.85	39.92	41.46	41.41	41.57	40.53
3	41.21	41.66	40.99	41.28	41.31	41.64	40.94	41.13	41.12	41.32
4	39.00	40.07	40.59	40.68	40.15	40.24	41.80	41.88	41.57	40.19
5	35.42	37.57	37.08	37.68	37.17	37.82	37.09	37.47	36.82	37.19
6	37.61	38.65	36.94	39.95	40.16	40.82	40.63	41.06	40.78	41.03
7	40.51	41.74	41.72	42.09	41.94	42.16	41.49	41.64	41.57	41.47
8	33.77	35.35	31.85	35.13	37.25	37.56	37.76	37.97	36.78	37.65
9	40.93	41.91	40.51	42.02	42.31	42.48	41.70	41.85	41.56	42.23
10	40.58	42.07	41.49	42.12	41.96	42.56	42.18	42.56	42.23	42.66
11	37.53	39.29	38.07	39.74	39.87	40.19	40.78	41.01	40.41	40.09
12	41.68	42.68	41.11	43.10	43.55	43.81	43.81	43.94	43.55	43.84
13	31.36	34.42	34.06	34.93	34.61	34.97	34.88	35.10	35.11	35.16
14	35.29	35.91	35.31	35.55	35.54	35.64	35.73	35.80	35.87	34.97
15	37.84	39.35	39.41	39.45	39.15	39.45	40.24	40.44	40.06	39.22
16	41.47	41.87	39.74	43.78	43.80	44.35	44.10	44.42	44.47	44.48
17	39.23	41.49	40.93	41.32	41.27	41.62	41.26	41.50	40.97	41.05
18	34.47	37.24	36.78	37.01	36.75	36.98	36.82	36.96	37.06	36.80
19	38.35	39.90	36.49	40.27	41.16	41.32	41.32	41.41	40.60	41.26
20	39.03	40.69	39.75	40.15	40.88	41.18	40.74	40.93	40.28	41.12
21	36.56	38.97	37.47	38.70	39.82	40.08	40.07	40.21	40.22	39.85
22	36.35	37.90	36.98	37.76	38.27	38.30	38.29	38.31	38.23	38.24
23	41.69	41.92	41.83	41.99	42.10	42.20	42.19	42.22	42.28	41.85
24	32.97	34.67	34.32	34.66	35.03	35.34	35.28	35.42	35.37	35.38
Average	37.80	39.28	38.26	39.47	39.72	40.01	40.04	40.21	39.94	39.93

The test images:

Kodak Lossless True Color Image Suite, http://r0k.us/graphics/kodak/

The demosaicking methods:

[Homo] K. Hirakawa and T. W. Parks. "Adaptive homogeneity-directed demosaicing algorithm", IEEE Trans. Image Process, Vol. 14, no. 3, pp. 360-369, 2005.

[POCS] B.K. Gunturk, Y. Altunbasak, and R.M. Mersereau. "Color plane interpolation using alternating projections", IEEE Trans. Image Processing, Vol. 11, no. 9, pp. 997-1013, 2002.

[Naive] Simply average the filtered chroma components at different frequency points.

[Adapt] E. Dubois. "Frequency-domain methods for demosaicking of Bayersampled color images", IEEE Signal Processing Letters, Vol. 12, no. 12, pp. 847-850, 2005. (http://www.site.uottawa.ca/~edubois/demosaicking/)

- and - D. Alleysson, S. Susstrunk, and J. Herault. "Linear demosaicing inspired by the human visual system". IEEE Trans. Image Processing, Vol. 14, no. 4, pp. 439-449, 2005.

The CFA patterns:

[Bayer] B.E. Bayer. "Color imaging array". U.S. Patent 3 971 065, 1976.

[CFA4a] a newly designed CFA pattern of size 4x4

[CFA4b] another newly designed CFA pattern of size 4x4

[CFA6] a newly designed CFA pattern of size 6x6

[CFA23] a newly designed CFA pattern of size 23x23