Multi-Resolution Subspace Reconstruction Through Density Measure - Application to Image Processing

A novel image subspace reconstruction has been proposed. The suggested inverse problem regularization algorithm approximates a class of differentials of function through multi-resolution density measure over level sets to learn high order- TV regularization operator, progressively. For this purpose, a differential spectral spectrum decomposition based on modulation theorem has been developed. The proposed methodology employs the relaxed upper gradient definition in the bounded variation and topological spaces to prove the stability and reliability of the proposed algorithm. We show that the resultant density measurement over sets define the higher-order bounded variation space such that the sequence of mean-value solutions are related to the relaxed upper gradient. Finally, numerical evaluations show the versatility of the proposed regularization algorithm applied to the image processing problems.