Zhang, Yin2011-07-252011-07-252010Li, Chengbo. "An efficient algorithm for total variation regularization with applications to the single pixel camera and compressive sensing." (2010) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/62229">https://hdl.handle.net/1911/62229</a>.https://hdl.handle.net/1911/62229In this thesis, I propose and study an efficient algorithm for solving a class of compressive sensing problems with total variation regularization. This research is motivated by the need for efficient solvers capable of restoring images to a high quality captured by the single pixel camera developed in the ECE department of Rice University. Based on the ideas of the augmented Lagrangian method and alternating minimization to solve subproblems, I develop an efficient and robust algorithm called TVAL3. TVAL3 is compared favorably with other widely used algorithms in terms of reconstruction speed and quality. Convincing numerical results are presented to show that TVAL3 is suitable for the single pixel camera as well as many other applications.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Applied mathematicsGeologyOperations researchThesisTHESIS COMP.SCI. 2010 LI