Hadamard multiplexing provides a considerable SNR boost over additive random noise but Poisson noise such as photon noise reduces the boost. We develop the theory for full H-matrix Hadamard transform imaging under additive and Poisson noise effects. We show that H-matrix encoding results in no effect on average on the noise level due to Poisson noise sources while preferentially reducing additive noise. We use this result to explain the wavelength-dependent varying SNR boost in a Hadamard hyperspectral imager and argue that such a preferential boost is useful when the main noise source is indeterminant or varying.
A hyperspectral imaging system is in development. The system uses spatially modulated Hadamard patterns to encode image information with implicit stray and ambient light correction and a reference beam to correct for source light changes over the spectral image capture period. In this study we test the efficacy of the corrections and the multiplex advantage for our system. The signal to noise ratio (SNR) was used to demonstrate the advantage of spatial multiplexing in the system and observe the effect of the reference beam correction. The statistical implications of the data acquisition technique, illumination source drift and correction of such drift, were derived. The reference beam correction was applied per spectrum before Hadamard decoding and alternately after decoding to all spectra in the image. The reference beam method made no fundamental change to SNR, therefore we conclude that light source drift is minimal and other possibly rectifiable error sources are dominant. The multiplex advantage was demonstrated ranging from a minimum SNR boost of 1.5 (600-975 nm) to a maximum of 11 (below 500 nm). Intermediate SNR boost was observed in 975-1700 nm. The large variation in SNR boost is also due to some other error source.
The model for Poisson random noise under Hadamard multiplexing is revised. The new model accounts for the variation of the Hadamard multiplexed measurements, as well as the previously considered variation due to Poisson fluctuations. A numerical simulation matches the model prediction within uncertainty.
This is the first of two papers dealing with a new conceptual model of fiber breakage in carding. This model is a departure from the integrated approach previously taken by one of the authors, and instead builds up the description of fiber length distributions after carding from the contributions of individual fibers. This paper first develops the underlying conceptual model of how carding affects individual fibers, and sets up the basis for a computer simulation model to be developed from the theoretical model.
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