A spectrum-recovery method is presented which efficiently computes an optimal unbiased linear spectrum-estimate for measurements obtained with Hadamard transform (HT) spectrometers having nonideal masks. This method has the following advantages over other spectrum-recovery techniques: it is computationally efficient, it requires no additional measurements, and it computes an optimal spectrum-estimate. In the method presented, after the mask of the HT spectrometer has been characterized, approximately 3<i>N</i> preliminary arithmetic operations are performed once for a given spectrometer, where <i>N</i> is both the number of spectral resolution-elements desired and the number of measurements required. Each spectrum-estimate to be recovered then requires only an additional <i>O</i>[<i>N</i>(log<sub>2</sub><i>N</i> + 4)] arithmetic operations. In contrast, conventional methods for obtaining an optimal unbiased linear spectrum-estimate require <i>O</i>(<i>N</i><sup>3</sup>) preliminary operations, and <i>O</i>(2<i>N</i><sup>2</sup>) operations during each spectrum-recovery.
T. W. Johnson, J. B. Park, S. A. Dyer, B. K. Harms, and R. A. Dyer, "An Efficient Method for Recovering the Optimal Unbiased Linear Spectrum-Estimate from Hadamard Transform Spectrometers Having Nonideal Masks," Appl. Spectrosc. 43, 746-750 (1989)