Wavelet Crosstalk Matrix and Its Application to Assessment of Shift-Variant Imaging Systems

J. Qi, R.H. Huesman
2004 IEEE Transactions on Nuclear Science  
The objective assessment of image quality is essential for design of imaging systems. Barrett and Gifford [1] introduced the Fourier crosstalk matrix. Because it is diagonal for continuous linear shift-invariant imaging systems, the Fourier crosstalk matrix is a powerful technique for discrete imaging systems that are close to shift invariant. However, for a system that is intrinsically shiftvariant, Fourier techniques are not particularly effective. Because Fourier bases have no localization
more » ... operty, the shift-variance of the imaging system cannot be shown by the response of individual Fourier bases; rather, it is shown in the correlation between the Fourier coefficients. This makes the analysis and optimization quite difficult. In this paper, we introduce a wavelet crosstalk matrix based on wavelet series expansions. The wavelet crosstalk matrix allows simultaneous study of the imaging system in both the frequency and spatial domains. Hence it is well suited for shiftvariant systems. We compared the wavelet crosstalk matrix with the Fourier crosstalk matrix for several simulated imaging systems, namely the interior and exterior tomography problems, limited angle tomography, and a rectangular geometry positron emission tomograph. The results demonstrate the advantages of the wavelet crosstalk matrix in analyzing shift-variant imaging systems.
doi:10.1109/tns.2003.822997 fatcat:6pmoimr5vvavlgpkazhfjhyfaa