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.

Masking, Photobleaching, and Spreading Effects in Hadamard Transform Imaging and Spectroscopy Systems

“…These can be errors due to under-or over-cutting the mask, 16 from m isaligned or moving m asks, 2 from temporal errors in stationary liquid crystal m asks, 17 and from absorption in the mask. 18,19 Each of these cases has been documented for speci c Ssequences, and m ethods for correcting the errors have been described. In addition to mask problems, Chen et al 20 obser ved that severe photobleaching interfered with the ability to recover the uorescence intensity of a Hadamard encoded image.…”