Towards Optimal Design of Time and Color Multiplexing Codes

Tsung-Han Chan^{1, 2}, Kui Jia¹, Eliot Wycoff¹, Chong-Yung Chi², and Yi Ma^{3, 4}

¹Advanced Digital Sciences Center, Singapore
Th.chan@adsc.com.sg
Chris.jia@adsc.com.sg
Eliot.wycoff@adsc.com.sg

²Inst. Communications Eng., National Tsing Hua University, Taiwan

³Microsoft Research Asia, Beijing, China
mayi@microsoft.com

⁴Dept. Elect. and Computer Eng., University of Illinois at Urbana-Champaign, USA

Abstract. Multiplexed illumination has been proved to be valuable and beneficial, in terms of noise reduction, in wide applications of computer vision and graphics, provided that the limitations of photon noise and saturation are properly tackled. Existing optimal multiplexing codes, in the sense of maximum signal-to-noise ratio (SNR), are primarily designed for time multiplexing, but they only apply to a multiplexing system requiring the number of measurements (M) equal to the number of illumination sources (N). In this paper, we formulate a general code design problem, where M  N, for time and color multiplexing, and develop a sequential semi-definite programming to deal with the formulated optimization problem. The proposed formulation and method can be readily specialized to time multiplexing, thereby making such optimized codes have a much broader application. Computer simulations will discover the main merit of the method— a significant boost of SNR as M increases. Experiments will also be presented to demonstrate the effectiveness and superiority of the method in object illumination.

Keywords: Multiplexing codes, maximum SNR, convex optimization

LNCS 7577, p. 485 ff.

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