A number of hyperspectral (x, y, λ) imaging systems work on the principle of limited angle tomography. In such systems there exists a region of spatial and spectral frequencies called the "missing cone" that the imaging system cannot recover from data using any direct reconstruction algorithms. Wavelets are useful for imaging objects that are spatially and in many cases also spectrally compact. However wavelet expansion functions have three-dimensional frequency content intersecting the missing cone region; this means the wavelets themselves are altered thus compromising the corresponding datacube reconstructions. As the missing cone of frequencies is fixed for a given imaging system, it is reasonable to adjust parameters in the wavelets themselves in order to reduce the intersection between the wavelets' frequency content and the missing cone. One wavelet system is better than another when the frequency content of the former has a smaller amount of overlap with the missing cone. We will do this analysis with a couple of classic wavelet families, the Morlet and the Difference of Gaussian (DOG) for an existing hyperspectral tomographic imaging system to show the feasibility of this procedure.

Date Published: 23 August 2010
PDF: 12 pages
Proc. SPIE 7799, Mathematics of Data/Image Coding, Compression, and Encryption with Applications XII, 779903 (23 August 2010); doi: 10.1117/12.862131

Published in SPIE Proceedings Vol. 7799:
Mathematics of Data/Image Coding, Compression, and Encryption with Applications XII
Mark S. Schmalz; Gerhard X. Ritter; Junior Barrera; Jaakko T. Astola, Editor(s)