Frame is the corner stone for designing decomposition and reconstruction operations in signal processing. Famous frames include wavelets, curvelets, and Gabor. A celebrated result indicates that if a synthesis frame is chosen for reconstruction, then its canonical dual frame is the analysis frame that performs decomposition, yielding coefficients that minimizes l2-norm of all coefficients of al...

Article history: Received 7 June 2011 Revised 7 December 2011 Accepted 30 December 2011 Available online 3 January 2012 Communicated by Karlheinz Gröchenig

In this paper we introduce and study Besselian $g$-frames. We show that the kernel of associated synthesis operator for a Besselian $g$-frame is finite dimensional. We also introduce $alpha$-dual of a $g$-frame and we get some results when we use the Hilbert-Schmidt norm for the members of a $g$-frame in a finite dimensional Hilbert space.

Background modeling is an important step in moving object detection and tracking. In this paper, we propose a new statistical approach in which, a sequence of frames are selected according to velocity and direction of some moving objects and then an initial background is modeled, based on the detection of gray pixel's value changes. To have used this sequence of frames, no estimator or distribu...

In this paper, we introduced and characterized the controlled $g$-duals of a frame in separable Hilbert space $\mathcal{H}$ . Afterwards, obtained new $C$-controlled $g$-dual frames from given frames. addition, approximation for was defined some their properties were investigated. Finally, relationship between approximately dual $g$-dual.

The berization of a ne systems via dual Gramian techniques, that was developed in previous papers of the authors, is applied here for the study of a ne frames which have an a ne dual system. Gramian techniques are also used to verify whether a dual pair of a ne frames is a also a pair of bi-orthogonal Riesz bases. A general method for a painless derivation of a dual pair of a ne frames from an ...

In this paper, we proposed a stretchable radio frequency (RF) sensor to detect strain direction and level. The stretchable sensor is composed of two complementary split ring resonators (CSRR) with microfluidic channels. In order to achieve stretchability, liquid metal (eutectic gallium-indium, EGaIn) and Ecoflex substrate are used. Microfluidic channels are built by Ecoflex elastomer and microf...

Approximately dual frames are studied in the Hilbert space setting. Approximate duals are easier to construct than classical dual frames, and can be tailored to yield almost perfect reconstruction. Bounds on the deviation from perfect reconstruction are obtained for approximately dual frames constructed via perturbation theory. An alternative bound is derived for the rich class of Gabor frames,...