Inthispaper,twoframeletbaseddeconvolutionalgorithmsareproposed.Thebasicideaofframeletbasedapproachistoconvertthedeconvolutionproblemtotheproblemofinpaintinginaframedomainbyconstructingaframeletsystemwithoneofthemasksbeingthegiven(discrete)convolutionkernelviatheunitaryextensionprincipleof[26],asintroducedin[6-9].Thefirstalgorithmunifiesourpreviousworksinhighresolutionimagereconstructionandinfra-redchoppedandnoddedimagerestoration,andthesecondoneisacombinationofourpreviousframe-baseddeconvolutionalgorithmandtheiterativethresholdingalgorithmgivenby[14,16].Thestrongconvergenceofthealgorithmsininfinitedimensionalsettingsisgivenbyemployingproximalforward-backwardsplitting(PFBS)method.Consequently,itunifiesiterativealgorithmsofinfiniteandfinitedimensionalsettingandsimplifiestheproofoftheconvergenceofthealgorithmsof[6].
