Duality between noise and spatial resolution in linear systems.
It is shown that in a broad class of linear systems, including general linear shift-invariant systems, the spatial resolution and the noise satisfy a duality relationship, resembling the uncertainty principle in quantum mechanics. The product of the spatial resolution and the standard deviation of output noise in such systems represents a type of phase-space volume that is invariant with respect to linear scaling of the point-spread function, and it cannot be made smaller than a certain positive absolute lower limit. A corresponding intrinsic "quality" characteristic is introduced and then evaluated for the cases of some popular imaging systems, including computed tomography, generic image convolution and phase-contrast imaging. It is shown that in the latter case the spatial resolution and the noise can sometimes be decoupled, potentially leading to a substantial increase in the imaging quality.
Timur E
TE
Gureyev
Yakov I
YI
Nesterets
Frank
F
de Hoog
Gerd
G
Schmalz
Sheridan C
SC
Mayo
Sara
S
Mohammadi
Giuliana
G
Tromba