Denoising analysis of Hadamard transform spectrometry.

We discuss denoising in Hadamard transform spectrometry (HTS) in terms of sensor noise, photon noise, and the sparsity of the source. An analysis based on spectra classification is proposed to estimate the signal-to-noise ratio (SNR) of both HTS and slit-based spectrometry. In contrast with previous theory, it is shown that HTS can improve the sensitivity of the sensor and that HTS outperforms slit-based spectrometry when the signal is dominated by photon noise and the source is sparse. Numerical simulations show that HTS is a good method for improving the poor SNR associated with weak or sparse signals.