Conventional approach in acquisition and reconstruction of images from frequency domain strictly follow the Nyquist sampling theorem. The... Show moreConventional approach in acquisition and reconstruction of images from frequency domain strictly follow the Nyquist sampling theorem. The principle states that the sampling frequency required for complete reconstruction of a signal is at least twice the maximum frequency of the original signal. This dissertation studies an emerging theory called Compressive Sensing or Compressive Sampling which goes against the conventional wisdom. Theoretically, it is possible to reconstruct images or signals accurately from a number of samples which is far smaller than the Nyquist samples. Compressive Sensing has proven to have farther implications than merely reducing sampling frequency of the signal. Possibility of new data acquisition methods from analog domain to digital form using fewer sensors, image acquisition using much smaller sensors array, to name a few. This novel theory combines sampling and compression methods thereby reducing the data acquisition resources, such as number of sensors, storage memory for collected samples and maximum operating frequency. This dissertation presents some insights into reconstruction of grey scale images and audio signals using OMP and CoSaMP algorithms. It also delves into some of the key mathematical insights underlying this new theory and explains some of the interactions between Compressive Sensing and related elds such as statistics, coding theory and theoretical computer science. viii M.S. in Computer Engineering, July 2014 Show less
