Wavelet crosstalk matrix and its application to assessment of shift-variant imaging systems

The objective assessment of image quality is essential for the design of imaging systems. Barrett and Gifford (1994) 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 shift-variant, Fourier techniques are not particularly effective. Because Fourier bases have no localization property, 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 shift-variant systems. We compared the wavelet crosstalk matrix with the Fourier crosstalk matrix 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.