Periodic multiresolution analyses in the space of periodic complex-valued functions an integer argument are studied. A characterization terms Fourier coefficients forming a scaling sequence is obtained. An example analysis with that consists trigonometric polynomials minimal possible spectrum presented. wavelet system associated such

These tutorial notes provide an introduction, review, and discussion of the state-of-the-art on simplification methods, Level Of Detail, and multiresolution models for surface meshes, and of their applications. The problem of approximating a surface with a triangular mesh is formally introduced, and major simplification techniques are classified, reviewed, and compared. A general framework is i...

We explore the use of the singular value decomposition (SVD) in image compression. We link the SVD and the multiresolution algorithms. In [22] it is derived a multiresolution representation of the SVD decomposition, and in [15] the SVD algorithm and Wavelets are linked, proposing a mixed algorithm which roughly consist on applying firstly a discrete Wavelet transform and secondly the SVD algori...

We identify multiresolution subspaces giving rise via Hankel transforms to Bessel functions. They emerge as orthogonal systems derived from geometric Hilbert-space considerations, the same way the wavelet functions from a multiresolution scaling wavelet construction arise from a scale of Hilbert spaces. We study the theory of representations of the C ∗-algebra Oν+1 arising from this multiresolu...