Results 1 to 10 of about 2,412,507 (179)
Optimal dual frames and frame completions for majorization [PDF]
Applied and Computational Harmonic Analysis, 2013 In this paper we consider two problems in frame theory. On the one hand, given a set of vectors $\mathcal F$ we describe the spectral and geometrical structure of optimal completions of $\mathcal F$ by a finite family of vectors with prescribed norms, where optimality is measured with respect to majorization.
Mariano Andres Ruiz +5 more
openaire +6 more sources
Applied and Computational Harmonic Analysis, 2022 One of a key problems in signal reconstruction process with the use of frames is to find a dual frame. Typically, a canonical dual frame is used. However, there are many applications where this choice appears to be unfortunate. Due to that fact, it is necessary to develop a tool, which helps to find a suitable dual frame. In this paper we give a method
Alan Kamuda, Sergiusz Kużel
openaire +3 more sources
On the Dual Frame Induced by an Invertible Frame Multiplier [PDF]
Sampling Theory in Signal and Image Processing, 2016 Recently it has been established that given an invertible frame multiplier with semi-normalized symbol, a specific dual of any of the two involved frames can be determined for the inversion purpose. The inverse can be represented as a multiplier with the reciprocal symbol, this particular dual of one of the given frames, and any dual of the other frame.
Diana T. Stoeva, Peter Balazs
openaire +5 more sources
Archiv der Mathematik, 2014 The definition of dual fusion frame presents technical problems related to the domain of the synthesis operator. The notion commonly used is the analogous to the canonical dual frame. Here a new concept of dual is studied in infinite-dimensional separable Hilbert spaces. It extends the commonly used notion and overcomes these technical difficulties. We
Heineken, Sigrid Bettina +3 more
openaire +4 more sources
The Canonical Dual Frame of a Wavelet Frame [PDF]
Applied and Computational Harmonic Analysis, 2002 AbstractIn this paper we show that there exist wavelet frames that have nice dual wavelet frames, but for which the canonical dual frame does not consist of wavelets, i.e., cannot be generated by the translates and dilates of a single function.
Bin Han, Ingrid Daubechies
openaire +1 more source
Oblique Dual Fusion Frames [PDF]
Numerical Functional Analysis and Optimization, 2018 We introduce and develop the concept of oblique duality for fusion frames. This concept provides a mathematical framework to deal with problems in distributed signal processing where the signals, considered as elements in a Hilbert space and under certain consistency requirements, are analyzed in one subspace and are reconstructed in another subspace.
Heineken, Sigrid Bettina +1 more
openaire +3 more sources
Approximate oblique dual frames
Applied Mathematics and Computation, 2023 In representations using frames, oblique duality appears in situations where the analysis and the synthesis has to be done in different subspaces. In some cases, we cannot obtain an explicit expression for the oblique duals and in others there exists only one oblique dual frame which has not the properties we need.
Diaz, Jorge Pablo +2 more
openaire +3 more sources
Involve, a Journal of Mathematics, 2013 The concept of frames in a Banach space has been introduced by Grochenig and developed by several authors. The main feature of a frame is to present every element of the underlying Banach space as a norm-convergent series. In this decomposition, the dual frame plays an essential role. The existence of a dual p-frame is not guaranteed in general.
Arefijamaal, Ali, Mohammadkhani, Leili
openaire +3 more sources
Communications, Faculty Of Science, University of Ankara Series A1Mathematics and Statistics, 2010 Serret-Frenet and Parallel-Transport frame are produced with thehelp of reel quaternions again by Andrew J. Hanson [7]. In this study, calculations mentioned above are applied for dual quaternion and Serret-Frenet andParallel-Transport frame are obtained by the aid of dual ...
ÖZTÜRK, Ufuk +3 more
openaire +3 more sources
The effect of perturbations of frames on their alternate and approximately dual frames [PDF]
Mathematical Methods in the Applied Sciences, 2021 Approximately dual frames as a generalization of duality notion in Hilbert spaces have applications in Gabor systems, wavelets, coorbit theory, and sensor modeling. In recent years, the computing of the associated deviations of the canonical and alternate dual frames from the original ones has been considered by functional analysts.
Hossein Javanshiri +2 more
openaire +3 more sources