| The wide usage of digital multimedia consumer electronics leads to the rapid explosion of the amount of image and video data for sharing, storage and transmission over networks. How to find efficient algorithms to process these data raises great challenges. Sparsity is a useful measurement of the efficiency. In this dissertation, we address these problems based on exploring the sparsity of data representations from data independent and data dependent perspectives.;In the first part of this dissertation, we study image representation using data independent approaches. For image representation, transforms can be used to convert original data into transform coefficients to eliminate the correlation among original data. We focus on images with singularities, which are very difficult to represent by conventional transforms.;We propose Ripplet transform type I (Ripplet-I), which generalizes Curvelet transform by introducing support and degree parameters. Curvelet transform is just a special case of Ripplet-I transform with c = 1, d = 2. Ripplet-I transform can represent images with singularities along arbitrary curves efficiently. Ripplet-I transform achieves sparser representation than Curvelet transform and demonstrates superior performance in applications such as image compression and image denoising.;Following the strategy of Ridgelet transform, we propose Ripplet transform type II (Ripplet-II) based on generalized Radon transform. Ripplet-II transform maps singularities along curves of images in the pixel domain to point singularities in the generalized Radon domain. Point singularities are further represented sparsely by wavelet transform. Ripplet-II transform has demonstrated better performance in image classification than conventional transforms.;In the second part of this dissertation, we study performance improving approaches by enhancing sparsity of image representations using the information from data. These approaches are data dependent and vary from case to case. To remove artifacts introduced by a video codec, we enhance the sparse representation of true signals to remove artifacts and preserve true signals; to improve video coding efficiency, we provide better intra prediction and adaptive block pattern to enhance the sparsity of residuals; to provide videos with smooth quality, we propose sparsity based rate control algorithm for video coding with constraints on distortion fluctuations. |
