title: Improved Compressive Sensing of Natural Scenes Using Localized Random Sampling.
abstract: Compressive sensing (CS) theory demonstrates that by using uniformly-random sampling, rather than uniformly-spaced sampling, higher quality image reconstructions are often achievable. Considering that the structure of sampling protocols has such a profound impact on the quality of image reconstructions, we formulate a new sampling scheme motivated by physiological receptive field structure, localized random sampling, which yields significantly improved CS image reconstructions. For each set of localized image measurements, our sampling method first randomly selects an image pixel and then measures its nearby pixels with probability depending on their distance from the initially selected pixel. We compare the uniformly-random and localized random sampling methods over a large space of sampling parameters, and show that, for the optimal parameter choices, higher quality image reconstructions can be consistently obtained by using localized random sampling. In addition, we argue that the localized random CS optimal parameter choice is stable with respect to diverse natural images, and scales with the number of samples used for reconstruction. We expect that the localized random sampling protocol helps to explain the evolutionarily advantageous nature of receptive field structure in visual systems and suggests several future research areas in CS theory and its application to brain imaging.
authors.affiliation: Department of Mathematics and Statistics, Swarthmore College, 500 College Avenue, Swarthmore, PA 19081, USA.
authors.forename: Victor J
authors.initials: VJ
authors.lastname: Barranca
authors.affiliation: Mathematical Sciences Department, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180, USA.
authors.forename: Gregor
authors.initials: G
authors.lastname: Kovačič
authors.affiliation: School of Mathematical Sciences, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China.
authors.forename: Douglas
authors.initials: D
authors.lastname: Zhou
authors.affiliation: School of Mathematical Sciences, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China.|Courant Institute of Mathematical Sciences and Center for Neural Science, New York University, New York, NY 10012, USA.|NYUAD Institute, New York University Abu Dhabi, PO Box 129188, Abu Dhabi, UAE.
authors.forename: David
authors.initials: D
authors.lastname: Cai