‎In this paper‎, ‎first we develop the duality concept for $g$-Bessel sequences‎ ‎and Bessel fusion sequences in Hilbert spaces‎. ‎We obtain some results about dual‎, ‎pseudo-dual ‎and approximate dual of frames and fusion frames‎. ‎We also expand every $g$-Bessel ‎sequence to a frame by summing some elements‎. ‎We define the restricted isometry property for ‎$g$-frames and generalize some resu...

In this paper, we study approximate duals of $g$-frames and fusion frames in Hilbert $C^ast-$modules. We get some relations between approximate duals of $g$-frames and biorthogonal Bessel sequences, and using these relations, some results for approximate duals of modular Riesz bases and fusion frames are obtained. Moreover, we generalize the concept of $Q-$approximate duality of $g$-frames and ...

A new type of grid turbulence generator, the 3D sparse (3DS), is a co-planar arrangement co-frames each containing different length scale elements [Malik, N. A. US Patent No. 9,599,269 B2 (2017)] and possessing much bigger parameter space than flat 2D fractal square (2DF). Using DNS we compare characteristics (mean flow, intensity, energy spectrum) generated by types 3DS grids. The peak intensi...

Planar object tracking plays an important role in AI applications, such as robotics, visual servoing, and SLAM. Although the previous planar trackers work well most scenarios, it is still a challenging task due to rapid motion large transformation between two consecutive frames. The essential reason behind this problem that condition number of non-linear system changes unstably when searching r...

$K$-frames as a generalization of frames were introduced by L. Gu{a}vruc{t}a to study atomic systems on Hilbert spaces which allows, in a stable way, to reconstruct elements from the range of the bounded linear operator $K$ in a Hilbert space. Recently some generalizations of this concept are introduced and some of its difference with ordinary frames are studied. In this paper, we give a new ge...

Controlled frames in Hilbert spaces have been recently introduced by P. Balazs and etc. for improving the numerical efficiency of interactive algorithms for inverting the frame operator. In this paper we develop a theory based on g-fusion frames on Hilbert spaces, which provides exactly the frameworks not only to model new frames on Hilbert spaces but also for deriving robust operators. In part...

Motion computation in scenes having multiple moving objects is performed together with object segmen-tation by using a temporal integration approach. Using an accurate 2D motion estimate for image regions, they can be enhanced by fusing all successive frames covering the same region. Enhancement includes improvement of image resolution and lling-in occluded regions. It is also shown how an accu...

The brightness patterns in two successive image frames are used to recover the motion of a planar object without computing the optical flow as an intermediate step. Based on a least-squares formulation, a set of nine nonlinear equations are derived. A simple iterative scheme for solving these equations is presented. Using a selected example, it is shown that in general, the scheme may converge ...