Fast delta Hadamard transform
In many fields (e.g., spectroscopy, imaging spectroscopy, photoacoustic imaging, coded aperture imaging) binary bit patterns known as m sequences are used to encode (by multiplexing) a series of measurements in order to obtain a larger throughput. The observed measurements must be decoded to obtain the desired spectrum (or image in the case of coded aperture imaging). Decoding in the past has used a technique called the fast Hadamard transform (FHT) whose chief advantage is that it can reduce the computational effort from N/sup 2/ multiplies of N log/sub 2/N additions or subtractions. However, the FHT has the disadvantage that it does not readily allow one to sample more finely than the number of bits used in the m sequence. This can limit the obtainable resolution and cause confusion near the sample boundaries (phasing errors). Both 1-D and 2-D methods (called fast delta Hadamard transforms, FDHT) have been developed which overcome both of the above limitations. Applications of the FDHT are discussed in the context of Hadamard spectroscopy and coded aperture imaging with uniformly redundant arrays. Special emphasis has been placed on how the FDHT can unite techniques used by both of these fields into the same mathematical basis.
- Research Organization:
- Los Alamos National Lab., NM
- OSTI ID:
- 6410503
- Journal Information:
- Appl. Opt.; (United States), Vol. 20:17
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
TRANSFORMATIONS
USES
CORRELATIONS
FORTRAN
MATHEMATICS
MATRICES
MULTIPLEXERS
ONE-DIMENSIONAL CALCULATIONS
RESOLUTION
SPECTROSCOPY
TWO-DIMENSIONAL CALCULATIONS
ELECTRONIC EQUIPMENT
EQUIPMENT
PROGRAMMING LANGUAGES
658000* - Mathematical Physics- (-1987)