‎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...

Segmentation is the first step in managing data for many information retrieval tasks. Automatic audio transcriptions and digital video footage are typically continuous data sources that must be pre-processed for segmentation into logical entities that can be stored, queried, and retrieved. Shot boundary detection is a common low-level video segmentation technique, where a video stream is divide...

Two standard tools for signal analysis are the short{time Fourier transform and the continuous wavelet transform. These tools arise as matrix coeecients of square integrable representations of the Heisenberg and aane groups respectively, and discrete frame decompositions of L 2 arise from approximations of corresponding reproducing formulae. Here we study two groups, the so-called aane Weyl-Hei...

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 ...

We develop a multi-modal/temporal logic for the analysis of a general class of continuous dynamical systems over arbitrary time-lines. Our frames consist of a topological space together with a flow (or group action), which is a function from the product of space and time into space that satisfies the two flow laws; we further require this function to be continuous. Over Euclidean space and real...

Advancements in deep learning and vision-based activity recognition development have significantly improved the safety, continuous monitoring, productivity, cost of earthwork site. The construction industry has adopted CNN RNN models to classify different activities equipment automate operations. However, currently available methods based on visual information current frames. To date, adjacent ...

$K$-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...

The use of human hand as a natural interface for humancomputer interaction (HCI) serves as the motivation for research in hand gesture recognition. Vision-based hand gesture recognition involves visual analysis of hand shape, position and/or movement. Due to co-articulation that occurs during transition from one gesture to the next, problem is encountered in continuous hand gesture recognition....

Nowadays, multimedia, especially video, is used widely in many domains. But camera lens are easily stained because they are always outside, such as in traffic and monitoring. Admittedly, the video from these cameras is out of action because it cannot provide clear frames. In this paper, we provide a detecting method from video with background restructure. This method is presented to detect stai...