title: Approximating filtered scale-variant signals.
abstract: We develop theorems that place limits on the point-wise approximation of the responses of filters, both linear shift invariant (LSI) and linear shift variant (LSV), to input signals and images that are LSV in the following sense: they can be expressed as the outputs of systems with LSV impulse responses, where the shift variance is with respect to the filter scale of a single-prototype fillter. The approximations take the form of LSI approximations to the responses. We develop tight bounds on the approximation errors expressed in terms of filter durations and derivative (Sobolev) norms. Finally, we find application of the developed theory to defoveation of images, deblurring of shift-variant blurs, and shift-variant edge detection.
authors.affiliation: Laboratory for Image and Video Engineering, Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, TX 78712-1084, USA.
authors.forename: Alan Conrad
authors.initials: AC
authors.lastname: Bovik
authors.forename: Raghu G
authors.initials: RG
authors.lastname: Raj
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D003196:Computer Graphics; D003198:Computer Simulation; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods; D015233:Models, Statistical; D009716:Numerical Analysis, Computer-Assisted; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted; D013382:Subtraction Technique