Image restoration through microlocal analysis with smooth tight wavelet frames (Theoretical development and feasibility of mathematical analysis on the computer)
Ryuichi Ashino, Steven J. Desjardins, Christopher Heil, Michihiro Nagase, Rémi Vaillancourt · Institutional Repositories DataBase (IRDB) · 2002
Results on general and tight wavelet frames and microlocal analysis in $\mathbb{R}^{n}$ are summarized.To perform microlocal analysis of tempered distributions in Rn, tight frame wavelets, whose Fourier transforms consist of smoothed characteristic functions of cubes in $\mathbb{R}^{n}$ , are constructed.Singularities in smooth images are localized in position and direction by means of frame coefficients computed in the Fourier d0- main.The numerical process of image restoration based on microlocal analysis with smooth tight wavelet frames is presented and two natural images are restored by this process.1Introduction In previous work [1], [2], [3], the concept of microlocal analysis was described, with the goal of numerically studying the singularities of distributions in $\mathbb{R}^{n}$ .