Yin, WotaoZhang, Yin2018-12-032018-12-032009Wang, Yilun. "Enhanced compressed sensing using iterative support detection." (2009) Diss., Rice University. <a href="https://hdl.handle.net/1911/103745">https://hdl.handle.net/1911/103745</a>.https://hdl.handle.net/1911/103745I present a new compressive reconstruction algorithm, which aims to simultaneously achieve low measurement requirement and fast reconstruction. This algorithm alternates between detecting partial support information of the true signal and solving a resulting truncated ℓ 1 minimization problem. I generalize Null Space Property to Truncated Null Space Property and exploit it for theoretical analysis of this truncated ℓ 1 minimization algorithm with Iterative Support Detection (abbreviated as ISD). Numerical results indicate the advantages of ISD over many other state of the art algorithms such as the basis pursuit (BP) model, the iterative reweighted ℓ 1 minimization algorithm (IRL1) and the iterative reweighted least squares algorithm (IRLS). Meanwhile, its limitation is demonstrated by both theoretical and experimental results.75 ppengCopyright 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 MathematicsElectrical engineeringApplied sciencesCompressed sensingIterative supportThesis751278593THESIS MATH. SCI. 2010 WANG