Abstract

Channel and memory capacities are limited and expensive resources in optical communication. In this work we propose several approaches to reduce the required capacity by using the a priori knowledge about the optical system used to capture the spatial information. The a priori knowledge is related to the triangularlike shape of the optical transfer function and to its spectral symmetry. In our work we will demonstrate a reduction in memory capacity required for the same image quality or a resolution enhancement for the same physical memory capacity. We will also present a nearly all-optical implementation of these techniques.

© 2010 Optical Society of America

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References

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2006

A. Shortt, T. J. Naughton, and B. Javidi, “Compression of digital holograms of three-dimensional objects using wavelets,” Opt. Express 14, 2625–2630 (2006).
[CrossRef] [PubMed]

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain,” Proc. SPIE 6065, 606509 (2006).
[CrossRef]

2005

2000

C. Christopoulos, A. Skodras, and T. Ebrahimi, “The JPEG2000 still image coding system: an overview,” IEEE Trans. Consumer Electron. 46, 1103–1127 (2000).
[CrossRef]

M. J. Weinberger, G. Seroussi, and G. Sapiro, “The LOCO-I lossless image compression algorithm: principles and standardization into JPEG-LS,” IEEE Trans. Image Process. 9, 1309–1324 (2000).
[CrossRef]

1991

1978

1973

1962

Ang, K. T.

Baraniuk, R. G.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain,” Proc. SPIE 6065, 606509 (2006).
[CrossRef]

Baron, D.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain,” Proc. SPIE 6065, 606509 (2006).
[CrossRef]

Burrows, M.

M. Burrows and D. J. Wheeler, “A block-sorting lossless data compression algorithm,” Tech. Rep. 124, Digital Systems Research Center, Palo Alto, California (1994).

Christopoulos, C.

C. Christopoulos, A. Skodras, and T. Ebrahimi, “The JPEG2000 still image coding system: an overview,” IEEE Trans. Consumer Electron. 46, 1103–1127 (2000).
[CrossRef]

Duarte, M. F.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain,” Proc. SPIE 6065, 606509 (2006).
[CrossRef]

Duvernoy, J.

Ebrahimi, T.

C. Christopoulos, A. Skodras, and T. Ebrahimi, “The JPEG2000 still image coding system: an overview,” IEEE Trans. Consumer Electron. 46, 1103–1127 (2000).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

Javidi, B.

Kelly, K. F.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain,” Proc. SPIE 6065, 606509 (2006).
[CrossRef]

Laska, J. N.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain,” Proc. SPIE 6065, 606509 (2006).
[CrossRef]

Lu, K.

Lukosz, W.

Naughton, T. J.

Ng, T. W.

Saleh, B. E. A.

Sapiro, G.

M. J. Weinberger, G. Seroussi, and G. Sapiro, “The LOCO-I lossless image compression algorithm: principles and standardization into JPEG-LS,” IEEE Trans. Image Process. 9, 1309–1324 (2000).
[CrossRef]

Sarvotham, S.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain,” Proc. SPIE 6065, 606509 (2006).
[CrossRef]

Seroussi, G.

M. J. Weinberger, G. Seroussi, and G. Sapiro, “The LOCO-I lossless image compression algorithm: principles and standardization into JPEG-LS,” IEEE Trans. Image Process. 9, 1309–1324 (2000).
[CrossRef]

Shortt, A.

Skodras, A.

C. Christopoulos, A. Skodras, and T. Ebrahimi, “The JPEG2000 still image coding system: an overview,” IEEE Trans. Consumer Electron. 46, 1103–1127 (2000).
[CrossRef]

Stoner, W.

Storer, J. A.

J. A. Storer, Image and Text Compression (Kluwer Academic, 1992).
[CrossRef]

Takhar, D.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain,” Proc. SPIE 6065, 606509 (2006).
[CrossRef]

Tribillon, G.

Tribillon, J. L.

Viénot, J. C.

Wakin, M. B.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain,” Proc. SPIE 6065, 606509 (2006).
[CrossRef]

Wallace, G. K.

G. K. Wallace, “The JPEG still picture compression standard,” Commun. ACM 34, 30–44 (1991).
[CrossRef]

Weinberger, M. J.

M. J. Weinberger, G. Seroussi, and G. Sapiro, “The LOCO-I lossless image compression algorithm: principles and standardization into JPEG-LS,” IEEE Trans. Image Process. 9, 1309–1324 (2000).
[CrossRef]

Wheeler, D. J.

M. Burrows and D. J. Wheeler, “A block-sorting lossless data compression algorithm,” Tech. Rep. 124, Digital Systems Research Center, Palo Alto, California (1994).

Appl. Opt.

Commun. ACM

G. K. Wallace, “The JPEG still picture compression standard,” Commun. ACM 34, 30–44 (1991).
[CrossRef]

IEEE Trans. Consumer Electron.

C. Christopoulos, A. Skodras, and T. Ebrahimi, “The JPEG2000 still image coding system: an overview,” IEEE Trans. Consumer Electron. 46, 1103–1127 (2000).
[CrossRef]

IEEE Trans. Image Process.

M. J. Weinberger, G. Seroussi, and G. Sapiro, “The LOCO-I lossless image compression algorithm: principles and standardization into JPEG-LS,” IEEE Trans. Image Process. 9, 1309–1324 (2000).
[CrossRef]

J. Opt. Soc. Am.

Opt. Express

Proc. SPIE

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain,” Proc. SPIE 6065, 606509 (2006).
[CrossRef]

Other

M. Burrows and D. J. Wheeler, “A block-sorting lossless data compression algorithm,” Tech. Rep. 124, Digital Systems Research Center, Palo Alto, California (1994).

J. A. Storer, Image and Text Compression (Kluwer Academic, 1992).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

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Figures (13)

Fig. 1
Fig. 1

Scheme of a generic communication system.

Fig. 2
Fig. 2

Different types of parallel-to-serial allocation. Allocation to serial vector (a) for the full spectrum and (b) for a quarter of the spectrum.

Fig. 3
Fig. 3

Spectrally nonuniform allocation of quantization bits.

Fig. 4
Fig. 4

Original image before being captured by the incoherent imaging system.

Fig. 5
Fig. 5

Incoherent imaging system characteristics: (a) pupil function and (b) OTF.

Fig. 6
Fig. 6

Scheme of system 1.

Fig. 7
Fig. 7

Scheme of system 2.

Fig. 8
Fig. 8

Images obtained in system 1 and system 2 for a maximal number of 4   bits per pixel.

Fig. 9
Fig. 9

Scheme of system 3.

Fig. 10
Fig. 10

Reconstructed images obtained at the receiver with 5   bits per pixel for (a) system 1 and (b) system 3.

Fig. 11
Fig. 11

Trade-off between RMS error and amount of bits. Reconstructed images obtained at the receiver for (a) system 1 using 6   bits , (b) system 1 using 8   bits , and (c) system 3 using 6   bits .

Fig. 12
Fig. 12

Reconstructed images obtained at the receiver for the same amount of information: (a) full spectrum as reference ( 3   bits per pixel) and (b) for system 3 ( 12   bits per pixel).

Fig. 13
Fig. 13

All-optical realization of the communication system parts: (a) conversion of the incoherent signal to the Fourier domain, (b) encoder, (c) decoder of the first two systems, (d) decoder of system 3.

Tables (1)

Tables Icon

Table 1 Comparison of the Amount of Information in the First Two Systems

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

u ˜ ( ν ) = u ˜ * ( ν ) ,
u ˜ ( ν ) = u ˜ + ( ν ) + u ˜ ( ν ) .
I ˜ OUT ( ν ) = I ˜ IN ( ν ) F ˜ ( ν ) ,
F ˜ ( ν ) = P ˜ ( ν + ν / 2 ) P ˜ * ( ν ν / 2 ) d ν ,
RMS = | A A ˜ | 2 ,
S = M · S W ,
S = M 1 N 1 + M 2 N 2 + M 3 N 3 ,

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