Analysis of a class of nonlinear and non-separable multiscale representations

作者：Matei Basarab; Meignen Sylvain^*

来源：Numerical Algorithms, 2012, 60(3): 391-418.

DOI：10.1007/s11075-011-9520-3

• Nonlinear multiscale representation
• Convergence
• Stability

In this paper, we introduce a particular class of nonlinear and non-separable multiscale representations which embeds most of these representations. After motivating the introduction of such a class on one-dimensional examples, we investigate the multi-dimensional and non-separable case where the scaling factor is given by a non-diagonal dilation matrix M. We also propose new convergence and stability results in L (p) and Besov spaces for that class of nonlinear and non-separable multiscale representations. We end the paper with an application of the proposed study to the convergence and the stability of some nonlinear multiscale representations.

• 出版日期2012-7