550 research outputs found
Restricted Isometries for Partial Random Circulant Matrices
In the theory of compressed sensing, restricted isometry analysis has become
a standard tool for studying how efficiently a measurement matrix acquires
information about sparse and compressible signals. Many recovery algorithms are
known to succeed when the restricted isometry constants of the sampling matrix
are small. Many potential applications of compressed sensing involve a
data-acquisition process that proceeds by convolution with a random pulse
followed by (nonrandom) subsampling. At present, the theoretical analysis of
this measurement technique is lacking. This paper demonstrates that the th
order restricted isometry constant is small when the number of samples
satisfies , where is the length of the pulse.
This bound improves on previous estimates, which exhibit quadratic scaling
Compressive Holographic Video
Compressed sensing has been discussed separately in spatial and temporal
domains. Compressive holography has been introduced as a method that allows 3D
tomographic reconstruction at different depths from a single 2D image. Coded
exposure is a temporal compressed sensing method for high speed video
acquisition. In this work, we combine compressive holography and coded exposure
techniques and extend the discussion to 4D reconstruction in space and time
from one coded captured image. In our prototype, digital in-line holography was
used for imaging macroscopic, fast moving objects. The pixel-wise temporal
modulation was implemented by a digital micromirror device. In this paper we
demonstrate temporal super resolution with multiple depths recovery
from a single image. Two examples are presented for the purpose of recording
subtle vibrations and tracking small particles within 5 ms.Comment: 12 pages, 6 figure
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