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- All Subjects: Sparse matrices
- Creators: Karam, Lina
Description
Spotlight mode synthetic aperture radar (SAR) imaging involves a tomo- graphic reconstruction from projections, necessitating acquisition of large amounts of data in order to form a moderately sized image. Since typical SAR sensors are hosted on mobile platforms, it is common to have limitations on SAR data acquisi- tion, storage and communication that can lead to data corruption and a resulting degradation of image quality. It is convenient to consider corrupted samples as missing, creating a sparsely sampled aperture. A sparse aperture would also result from compressive sensing, which is a very attractive concept for data intensive sen- sors such as SAR. Recent developments in sparse decomposition algorithms can be applied to the problem of SAR image formation from a sparsely sampled aperture. Two modified sparse decomposition algorithms are developed, based on well known existing algorithms, modified to be practical in application on modest computa- tional resources. The two algorithms are demonstrated on real-world SAR images. Algorithm performance with respect to super-resolution, noise, coherent speckle and target/clutter decomposition is explored. These algorithms yield more accu- rate image reconstruction from sparsely sampled apertures than classical spectral estimators. At the current state of development, sparse image reconstruction using these two algorithms require about two orders of magnitude greater processing time than classical SAR image formation.
ContributorsWerth, Nicholas (Author) / Karam, Lina (Thesis advisor) / Papandreou-Suppappola, Antonia (Committee member) / Spanias, Andreas (Committee member) / Arizona State University (Publisher)
Created2011
Description
Effective modeling of high dimensional data is crucial in information processing and machine learning. Classical subspace methods have been very effective in such applications. However, over the past few decades, there has been considerable research towards the development of new modeling paradigms that go beyond subspace methods. This dissertation focuses on the study of sparse models and their interplay with modern machine learning techniques such as manifold, ensemble and graph-based methods, along with their applications in image analysis and recovery. By considering graph relations between data samples while learning sparse models, graph-embedded codes can be obtained for use in unsupervised, supervised and semi-supervised problems. Using experiments on standard datasets, it is demonstrated that the codes obtained from the proposed methods outperform several baseline algorithms. In order to facilitate sparse learning with large scale data, the paradigm of ensemble sparse coding is proposed, and different strategies for constructing weak base models are developed. Experiments with image recovery and clustering demonstrate that these ensemble models perform better when compared to conventional sparse coding frameworks. When examples from the data manifold are available, manifold constraints can be incorporated with sparse models and two approaches are proposed to combine sparse coding with manifold projection. The improved performance of the proposed techniques in comparison to sparse coding approaches is demonstrated using several image recovery experiments. In addition to these approaches, it might be required in some applications to combine multiple sparse models with different regularizations. In particular, combining an unconstrained sparse model with non-negative sparse coding is important in image analysis, and it poses several algorithmic and theoretical challenges. A convex and an efficient greedy algorithm for recovering combined representations are proposed. Theoretical guarantees on sparsity thresholds for exact recovery using these algorithms are derived and recovery performance is also demonstrated using simulations on synthetic data. Finally, the problem of non-linear compressive sensing, where the measurement process is carried out in feature space obtained using non-linear transformations, is considered. An optimized non-linear measurement system is proposed, and improvements in recovery performance are demonstrated in comparison to using random measurements as well as optimized linear measurements.
ContributorsNatesan Ramamurthy, Karthikeyan (Author) / Spanias, Andreas (Thesis advisor) / Tsakalis, Konstantinos (Committee member) / Karam, Lina (Committee member) / Turaga, Pavan (Committee member) / Arizona State University (Publisher)
Created2013