Showing papers by "Manos Papadakis published in 2001"
TL;DR: In this article, a wavelet generator is constructed using the Continuous Wavelet Transform with repect to the scale parameter, taking the Gaussian function as the scaling function, and a numerical experiment is carried out demonstrating the use of the resulting wavelet for edge detection.
Abstract: This work investigates some mathematical properties of the Distributed Approximating Functionals (DAFs). We prove that certain classes of DAFs yield Unity Approximations. Two distinct classes which serve as examples are the Hermite-DAFs and the Sinc-class DAFs. Detailed proofs are given. A wavelet generator is constructed using the Continuous Wavelet Transform with repect to the scale parameter. Taking the Gaussian function as the scaling function, a numerical experiment is carried out demonstrating the use of the resulting wavelet for edge detection.
8 citations
05 Dec 2001
TL;DR: In this paper, the concept of frames of translates was introduced and the countable families of vectors generating such frames were characterized and generalized to generalized frame MRAs of L 2 (R).
Abstract: We introduce the concept of frames of translates and we characterize the countable families of vectors generating such frames. In this context we generalize the concept of the Grammian introduced by Ron and Shen. We apply this characterization to study Generalized frame MRAs of L 2 (R). We also provide the characterization of frame multiwavelet sets associated with GFMRAs of L 2 (R) and we present examples of GFMRAs.
3 citations