Tight frames and g-frames are extremely useful in applications. A SCALABLE frame was recentlyintroduced as a frame with the property of generating a tight frame by rescaling its frame vectors. In thispaper, we generalize this concept to g-frames, introduce SCALABLE g-frames, obtain some characterizationsfor them, and demonstrate that scalability is stable under unitary operators and isomorophisms betweentwo Hilbert spaces. In addition, we consider Paley-Wiener perturbations of g-frames and achieve someresults regarding the preservation of their g-frame property.

One of the important topics of passive defense is threats detection and waning alarm. One of the most widely used methods in detection field is video data investigation in order to identify unknown targets and warning alarm. In order to evaluate a fast and high-precision technique, video summarization is presented. Also, during the past years, creation of digital videos has caused exponential growth of video content. To increase the high volume of video usability, a lot of researches have been done and video summarization has been proposed to quick view of large video collection and quick understanding of the content of video data. In the video summarization, pictures are selected as a representative of each scene to obtain a visual overview of whole video. Recently, new methods using sparse formulation are suggested for video summarization being more effective in video data summarization than other methods. In this paper, video summarization is presented as a sparse dictionary selection problem. For this purpose, using a new method based on sparse coding, have been able to improve video data summarization compared to other video summarization methods based on sparse or other coding. Finally, the results for the ground truth data collection and State of the art methods, shows improvement our claim in the video summary on proposed method.