Learning-based multiresolution transforms with application to image compression

• In Harten's framework, multiresolution transforms are defined by two operators.
• The predictor operator predicts finer levels of information from coarser ones.
• Goal is to minimize the details: the difference between the exact and predicted values.
• We use statistical learning tools to design a more accurate prediction operator.
• With this approach we obtain improvements over standard multiresolution transforms.

In Harten's framework, multiresolution transforms are defined by predicting finer resolution levels of information from coarser ones using an operator, called prediction operator, and defining details (or wavelet coefficients) that are the difference between the exact and predicted values. In this paper we use tools of statistical learning in order to design a more accurate prediction operator in this framework based on a training sample, resulting in multiresolution decompositions with enhanced sparsity. In the case of images, we incorporate edge detection techniques in the design of the prediction operator in order to avoid Gibbs phenomenon. Numerical tests are presented showing that the learning-based multiresolution transform compares favorably with the standard multiresolution transforms in terms of compression capability.