Authors:
Paul Escande
;
Pierre Weiss
and
Francois Malgouyres
Affiliation:
Université de Toulouse and CNRS, France
Keyword(s):
Image Deblurring, Spatially Varying Blur, Operator Approximation, Wavelet Packet Transform, Bi-harmonic Spline Interpolation, Convex Optimization.
Related
Ontology
Subjects/Areas/Topics:
Applications
;
Bayesian Models
;
Bioinformatics and Systems Biology
;
Cardiovascular Imaging and Cardiography
;
Cardiovascular Technologies
;
Convex Optimization
;
Exact and Approximate Inference
;
Health Engineering and Technology Applications
;
Medical Imaging
;
Model Selection
;
Pattern Recognition
;
Signal Processing
;
Software Engineering
;
Theory and Methods
Abstract:
Restoration of images degraded by spatially varying blurs is an issue of increasing importance. Many new optical systems allow to know the system point spread function at some random locations, by using microscopic luminescent structures. Given a set of impulse responses, we propose a fast and efficient algorithm to reconstruct the blurring operator in the whole image domain. Our method consists in finding an approximation of the integral operator by operators diagonal in the wavelet domain. Interestingly, this method complexity scales linearly with the image size. It is thus applicable to large 3D problems. We show that this approach might outperform previously proposed strategies such as linear interpolations (Nagy and O’Leary, 1998) or separable approximations (Zhang et al., 2007). We provide various theoretical and numerical results in order to justify the proposed methods.