In a context marked by the proliferation of smartphones and multimedia applications, the processing and transmission of images have become a real problem. Image compression is the first approach to address this problem, it nevertheless suffers from its inability to adapt to the dynamics of limited environments, consisting mainly of mobile equipment and wireless networks. In this work, we propose a stochastic model to gradually estimate an image upon information on its pixels that are transmitted progressively. We consider this transmission as a dynamical process, where the sender pushes the data in decreasing significance order. In order to adapt to network conditions and performances, instead of truncating the pixels, we suggest a new method called Fast Reconstruction Method by Kalman Filtering (FRM-KF) consisting of recursive inference of the not yet received layers belonging to a sequence of bitplanes. After empirical analysis, we estimate parameters of our model which is a linear discrete Kalman Filter. We assume the initial law of information to be the uniform distribution on the set [0, 255] corresponding to the range of gray levels. The performances of FRM-KF method have been evaluated in terms of the ratios in the quality of data image/size sent and in the quality of image/time required for treatment. A high quality was reached faster with relatively small data (less than 10% of image data is needed to obtain up to the sixth-quality image). The time for treatment also decreases faster with number of received layers. However, we found that the time of image treatment might be large starting from a image resolution of 1024 *

The main objective of this work is to propose concrete time reduction strategies for discovery of Wi-Fi Direct in Android. To achieve our goals, we perform a fairly general mathematical modeling of the discovery of devices using Poisson processes. Subsequently, under asymptotic invariance hypotheses of certain distributions, we derive formulas for the expected time to discovery. We provide sufficient condition for fast convergence to an invariant distribution and determine key decision parameters (jumps intensities) that minimize the average time to discovery. We also propose a predictive model for rapid evaluation of these optimal discovery parameters. Experimental tests in an emulator are also conducted to validate the theoretical results obtained. A comparative performance study is done with some optimization approaches from literature. Compared with existing methods, the improvement of the average time discovery we obtained with the proposed method is above 98.34%.