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Compressed sensing and imaging

Student-Run Applied & Math Seminar

Speaker: Deanna Needell, Claremont McKenna College
Location: 2112 MSB
Start time: Wed, Dec 10 2014, 12:10PM

Compressed sensing is a new field which shows that reliable, nonadaptive data acquisition, with far fewer measurements than traditionally assumed, is possible. In this talk we will introduce the fundamental ideas behind compressed sensing, focusing on imaging techniques, as well as new results for imaging via total variation. Discrete images, composed of patches of slowly-varying pixel values, have sparse or compressible wavelet representations which allow the techniques from compressed sensing such as L1-minimization to be utilized. In addition, such images also have sparse or compressible discrete derivatives which motivate the use of total variation minimization for image reconstruction. Although image compression is a primary motivation for compressed sensing, stability results for total-variation minimization do not follow directly from the standard theory. In this talk, we present provable near-optimal reconstruction guarantees for total-variation minimization using properties of the bivariate Haar transform along with numerical studies demonstrating its advantages.