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8 October 2007 Model based compression of the calibration matrix for hyperspectral imaging systems
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Abstract
In hyperspectral imaging systems with a continuous-to-discrete (CD) model, the goal is to solve the matrix equation g = Hθ + n for θ. Here g is a data vector obtained on pixels on a focal plane array (FPA), and n is the additive pixel noise vector. The hyperspectral object cube f(x, y, λ) to be recovered is represented by θ, which is the vectorized set of expansion coefficients of f with respect to a family of functions. The imaging operator is the system matrix H of which its columns represent the projection of each expansion function onto the FPA. Hence an estimate of the object cube f(x, y, λ) is reconstructed from these recovered expansion function projection coefficients. Furthermore H is equivalently a calibration matrix, and amenable to an analytic description. Since the number of expansion functions is large, and the number of pixels on an FPA is large, H becomes huge and very unwieldy to store. We describe a means by which we can reduce the effective size of H by taking advantage of the analytic model of the imaging system and converting H into a series of look-up tables. By this method we have been able to drastically reduce the storage requirements for H from terabytes to sub-megabyte sizes. We provide an example of this technique in isoplanatic and polychromatic calibration of a flash hyperspectral imaging system. These sets of lookup tables are expansion function independent and also independent of object cube sampling.
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James F. Scholl, E. Keith Hege, Daniel O'Connell, and Eustace L. Dereniak "Model based compression of the calibration matrix for hyperspectral imaging systems", Proc. SPIE 6700, Mathematics of Data/Image Pattern Recognition, Compression, Coding, and Encryption X, with Applications, 670002 (8 October 2007); https://doi.org/10.1117/12.730848
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