This project intends to optimize several video encoding parameters. Although we focus on ITU-T H.264/MPEG-4 AVC standard as a reference to formulate the problems, all the optimization solutions to be investigated have a more general application. As it is well known, a standard like H.264 is a compilation of the most sophisticated algorithms. Despite each of them by itself is qualified as of a high performance, their combination may result in a poor system. For instance, a standard could provide either less or better performance in some circumstances like constant/variable bit rate (BR), low/high BR, low/high resolution, low/high scalability, good/bad channel, low/high delay, etc. Therefore, parameter tuning is of crucial importance to adapt the standard to any of those conditions. Moreover, in general, when a new standard is issued, it provides a worse performance than any previous one since it lacks optimization. This is the case of H.264, a recent ITU/MPEG standard with some profiles still to be approved. As the history showed, we then expect, in the ORAL framework, to contribute to improve H.264 performance significantly. The main motivation to embrace this proposed research is to join, in a fruitful manner, scientists from mathematics and communications to solve multidimensional telecom problems. The optimization problems to be processed are large-scale and involve constraints. Furthermore, interpolation, stability, existence, achievability and convergence rate are critical mathematical concepts that are fundamental in this research. Let Xijk be a random process defining an original sample (image pixel) at spatio-temporal position i,j,k of video sequence length T and image resolution NxM.
We intend to propose new mathematical methods for those specific problems in order to achieve optimal and sub-optimal solutions with as low computational complexity as possible. These new methodologies are to be compared with other solution methods that have been published in the literature.