PRESTRESS AND CONSTRUCTION ORDER OPTIMIZATION OF CABLE-SUPPORTED FRAMES

Construction of compactly supported affine frames

Since the publication, less than ten years ago, of Mallat’s paper on Multiresoltion Analysis [Ma], and Daubechies’ paper on the construction of smooth compactly supported refinable functions [D], wavelets had gained enormous popularity in mathematics and in the application domains. It is sufficient to note that there are currently more than 10,000 subscribers to the monthly Wavelet Digest. At t...

Construction of Compactly Supported Tight Wavelets Frames

Construction of continuous $g$-frames and continuous fusion frames

A generalization of the known results in fusion frames and $g$-frames theory to continuous fusion frames which defined by M. H. Faroughi and R. Ahmadi, is presented in this study. Continuous resolution of the identity (CRI) is introduced, a new family of CRI is constructed, and a number of reconstruction formulas are obtained. Also, new results are given on the duality of continuous fusion fram...

Construction of Multivariate Compactly Supported Tight Wavelet Frames

Two simple constructive methods are presented to compute compactly supported tight wavelet frames for any given refinable function whose mask satisfies the QMF or sub-QMF conditions in the multivariate setting. We use one of our constructive methods in order to find tight wavelet frames associated with multivariate box splines, e.g., bivariate box splines on a three or four directional mesh. Mo...

Construction of compactly Supported Conjugate Symmetric Complex Tight Wavelet Frames

Two algorithms for constructing a class of compactly supported complex tight wavelet frames with conjugate symmetry are provided. Firstly, based on a given complex refinable function φ, an explicit formula for constructing complex tight wavelet frames is presented. If the given complex refinable function φ is compactly supported conjugate symmetric, then we prove that there exists a compactly s...