document: A framework for image deblurring using wavelet packet bases We show that the average over translations of an operator diagonal in a wavelet packet basis is a convolution . We also show that an operator diagonal in a wavelet packet basis can be decomposed into several operators of the same kind , each of them being better conditioned . We investigate the possibility of using such a convolution to approximate a given convolution -LRB- in practice an image blur -RRB- . Then we use these approximations to deblur images . First , we show that this framework permits us to redefine existing deblurring methods . Then , we show that it permits us to define a new variational method which combines the wavelet packet and the total variation approaches . We argue and show by experiments that this permits us to avoid the drawbacks of both approaches which are , respectively , ringing and staircasing
doc_bio_tags: O O O B I O B I I O O O O O O O O O B I O O O O O O O B O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B
extractive_keyphrases: image deblurring wavelet packet bases convolution operator diagonal ringing staircasing
abstractive_keyphrases: total variation approach deconvolution