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Full-Text Articles in Physical Sciences and Mathematics
Unconstrained L1 Optimization With Applications To Signal And Image Processing, Carlos Andres Ramirez
Unconstrained L1 Optimization With Applications To Signal And Image Processing, Carlos Andres Ramirez
Open Access Theses & Dissertations
In recent years, the applied mathematical community has witnessed a revolution that is changing the paradigm of classical signal and image processing. Novel and e efficient numerical algorithms have emerged for solving new challenges in large scale signal retrieval, where both constrained and unconstrained L1 minimization methods play a fundamental role.
In this work, we present a new methodology for solving unconstrained L1 minimization problems in the context of image and signal processing. Our approach consists in solving a sequence of relaxed unconstrained minimization problems depending on a positive regularization parameter that converges to zero. The optimality conditions of each …
Digital Image Processing Based On Sparse Representation And Convex Programming, Carlos Andres Ramirez
Digital Image Processing Based On Sparse Representation And Convex Programming, Carlos Andres Ramirez
Open Access Theses & Dissertations
Sparse representation models have been of central interest in recent years due to important achievements in computational harmonic analysis, such as wavelet transformations, and the most recent sampling theory, compressed sensing. Numerous applications based on sparse models have been studied in the last decade leading to promising results. These applications include areas in seismology, image processing, wireless sensor networks, computed tomography and magnetic resonance imaging just to mention a few.
In this work, we propose to extend such applications in the area of image processing, particularly for the image segmentation problem, and examine algorithms involved in sparse modeling from both …