An Efficient Method for Recovering the Optimal Unbiased Linear Spectrum-Estimate from Hadamard Transform Spectrometers Having Nonideal Masks

Abstract

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 N preliminary arithmetic operations are performed once for a given spectrometer, where N 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 O[ N(log₂ N + 4)] arithmetic operations. In contrast, conventional methods for obtaining an optimal unbiased linear spectrum-estimate require O( N³) preliminary operations, and O(2 N²) operations during each spectrum-recovery.