Compressive Sensing applied on a Video Signal

Sammanfattning: Compressive Sensing has attracted a lot of attention over the last decade within the areas of applied mathematics, computer science and electrical engineering because of it suggesting that we can sample a signal under the limit that traditional sampling theory provides. By then using dierent recovery algorithms we are able to, theoretically, recover the complete original signal even though we have taken very few samples to begin with. It has been proven that these recovery algorithms work best on signals that are highly compressible, meaning that the signals can have a sparse representation where the majority of the signal elements are close to zero. In this thesis we implement some of these recovery algorithms and investigate how these perform practically on a real video signal consisting of 300 sequential image frames. The video signal will be under sampled, using compressive sensing, and then recovered using two types of strategies, - One where no time correlation between successive frames is assumed, using the classical greedy algorithm Orthogonal Matching Pursuit (OMP) and a more robust, modied OMP called Predictive Orthogonal Matching Pursuit (PrOMP). - One newly developed algorithm, Dynamic Iterative Pursuit (DIP), which assumes and utilizes time correlation between successive frames. We then performance evaluate and compare these two strategies using the Peak Signal to Noise Ratio (PSNR) as a metric. We also provide visual results. Based on investigation of the data in the video signal, using a simple model for the time correlation and transition probabilities between dierent signal coecients in time, the DIP algorithm showed good recovery performance. The main results showed that DIP performed better and better over time and outperformed the PrOMP up to a maximum of 6 dB gain at half of the original sampling rate but performed slightly below the PrOMP in a smaller part of the video sequence where the correlation in time between successive frames in the original video sequence suddenly became weaker.