Optimal transformations for optical multiplex measurements in the presence of photon noise

Wuttig, Andreas

doi:10.1364/ao.44.002710

Cited by 28 publications

(36 citation statements)

References 4 publications

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“…Mutting [10] looked into the effect of photon noise to Hadamard multiplexing, and derived new multiplexing codes, based on two-level autocorrelation sequences. These multiplexing codes have shown their advantages when there are photon noise, but they are only available for a very limit set of N and for limit range of noise variances {σ 2 , ρ 2 }.…”

Section: Related Workmentioning

confidence: 99%

“…Recall the time multiplexing model (1), where A becomes M × N instead of N × N conventionally addressed in the previous works [1,2,4,10,11]. Following the similar derivations in (11), (12), (13) and (14), the design of such A ∈ R M×N is to solve the optimization problem {A , P } = arg min…”

Section: Application Of Algorithm 1 To Time Multiplexingmentioning

confidence: 99%

“…When the photon noise comes into play, multiplexing multiple light sources may become counterproductive [10]. Present efforts for designing multiplexing codes in the presence of both sensor noise and photon noise include the works in [10][11][12], but they are limited to time multiplexing system where the number of measurements (M ) equals the number of illumination sources (N ). Some questions may arise: How to design the multiplexing codes for the system not only applying time multiplexing but also color multiplexing?…”

Section: Introductionmentioning

confidence: 99%

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Towards Optimal Design of Time and Color Multiplexing Codes

Chan

Jia

Wycoff

et al. 2012

Computer Vision – ECCV 2012

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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.

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Section: Related Workmentioning

confidence: 99%

Section: Application Of Algorithm 1 To Time Multiplexingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Towards Optimal Design of Time and Color Multiplexing Codes

Chan

Jia

Wycoff

et al. 2012

Computer Vision – ECCV 2012

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“…Also, as a side effect, the raw images do not show any evident spectral features, which makes them more suitable for image reconstruction techniques Such applications of Hadamard techniques to spectropolarimetry are however hindered by the known fact that, in the presence of a multiplicative noise such as photonic noise, the Hadamard transformation results in a reduction of SNRs with respect to the case of equivalent exposures without multiplexing (Harwit & Sloane 1979). The reduction in the SNR can be limited with the use of appropriate binary masks (Wuttig 2005), although it is never too large for the usual cases in solar spectropolarimetry.…”

Section: Efficient Spectro-imagersmentioning

confidence: 99%

Compressive sensing for spectroscopy and polarimetry

Ramos

Ariste²

2010

A&A

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We demonstrate, through numerical simulations with real data, the feasibility of using compressive sensing techniques for the acquisition of spectro-polarimetric data. This allows us to combine the measurement and the compression process into one consistent framework. Signals are recovered using a sparse reconstruction scheme from projections of the signal of interest onto appropriately chosen vectors, typically noise-like vectors. The compressibility properties of spectral lines are analyzed in detail. The results shown in this paper demonstrate that, thanks to the compressibility properties of spectral lines, it is feasible to reconstruct the signals using only a small fraction of the information that is measured nowadays. We investigate in depth the quality of the reconstruction as a function of the amount of data measured and the influence of noise. This change of paradigm also allows us to define new instrumental strategies and to propose modifications to existing instruments in order to take advantage of compressive sensing techniques.

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“…When considering photon noise along with sensor noise, multiplexing multiple light sources may be counterproductive [9]. Present efforts for designing max-SNR multiplexing codes in the presence of both sensor noise and photon noise include [9]- [11], but they are limited to time multiplexing systems where the number of measurements equals the number of illumination sources . Some questions then arise: what can we gain from multiplexing if the number of measurements is larger than the number of illumination sources ?…”

Section: Introductionmentioning

confidence: 99%

MMSE Design of Time and Color Multiplexing Codes

Chan

Jia

Wycoff

et al. 2014

IEEE Trans. Signal Process.

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Abstract-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 to be equal to the number of illumination sources . 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 , where 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 increases. Experiments also demonstrate the effectiveness and superiority of the proposed method in illuminating various objects.Index Terms-Optical multiplexing, maximum signal-to-noise ratio (SNR), minimum mean square error (MMSE), sequential convex approximation, time and color.

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Optimal transformations for optical multiplex measurements in the presence of photon noise

Cited by 28 publications

References 4 publications

Towards Optimal Design of Time and Color Multiplexing Codes

Towards Optimal Design of Time and Color Multiplexing Codes

Compressive sensing for spectroscopy and polarimetry

MMSE Design of Time and Color Multiplexing Codes

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