Curvelet transform with adaptive tiling

In this dissertation we address the problem of adapting frequency domain tiling using the curvelet transform as the basis algorithm. The optimal tiling, for a given class of images, is computed using denoising performance as the cost function. The major adaptations considered are: the number of scale decompositions, angular decompositions per scale/quadrant, and scale locations. A global optimization algorithm combining the three adaptations is proposed. Denoising performance of adaptive curvelets is tested on seismic and face data sets. The developed adaptation procedure is applied to a number of different application areas. Adaptive curvelets are used to solve the problem of sparse data recovery from subsampled measurements. Performance comparison with default curvelets demonstrates the effectiveness of the adaptation scheme. Adaptive curvelets are also used in the development of a novel image similarity index. The developed measure succeeds in retrieving correct matches from a variety of textured materials. Furthermore, we present an algorithm for classifying different types of seismic activities.Ph.D