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.
© 2014 Optical Society of America
Original Manuscript: March 12, 2014
Revised Manuscript: May 16, 2014
Manuscript Accepted: May 16, 2014
Published: June 18, 2014
Jiang Yue, Jing Han, Yi Zhang, and Lian-Fa Bai, "Denoising analysis of Hadamard transform spectrometry," Opt. Lett. 39, 3744-3747 (2014)