Non-consistent cell-average multiresolution operators with application to image processing

In recent years different techniques to process signal and image have been designed and developed. In particular, multiresolution representations of data have been studied and used successfully for several applications such as compression, denoising or inpainting. A general framework about multiresolution representation has been presented by Harten (1996) [20]. Harten's schemes are based on two operators: decimation, D, and prediction, P, that satisfy the consistency property DP=I, where I is the identity operator. Recently, some new classes of multiresolution operators have been designed using learning statistical tools and weighted local polynomial regression methods obtaining filters that do not satisfy this condition. We show some proposals to solve the consistency problem and analyze its properties. Moreover, some numerical experiments comparing our methods with the classical methods are presented.