MMSE Design of Time and Color Multiplexing Codes

Illumination multiplexing has proven itself to be a valuable tool in image quality improvement for many computer vision and graphics applications, provided that its limitations on photon noise and saturation are properly tackled. Currently, multiplexing codes are constructed according to the maximum signal-to-noise ratio (SNR), and they are primarily employed for time multiplexing, a technique that requires the number of measurements M to be equal to the number of illumination sources N. In this work, we propose an illumination multiplexing method based on minimum mean square errors (MMSEs) for the more general setting of both time and color multiplexing performed together, with KM ≥ N, where K is the number of color channels. Under the umbrella of the proposed MMSE formulation, the conventional maximum SNR approach can be thought of as a special case of the MMSE design. The formulated MMSE problem is a difficult non-convex problem, but it can be approximated by sequential semi-definite (convex) programming and a 1-D exhaustive search. The proposed formulation and algorithm can be readily specialized to max-SNR and/or time multiplexing designs, thereby giving the optimized codes a much broader scope of application. Computer simulations show that the conventional max-SNR design is suboptimal to the proposed MMSE design, though both see significant quality improvements as M increases. Experiments also demonstrate the effectiveness and superiority of the proposed method in illuminating various objects.