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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 Hadamarddoi:10.1364/ao.48.002078 pmid:19363545 fatcat:rhyk3dlza5a6lo4xlrfxvoo4s4