11,520 research outputs found
High-quality Image Restoration from Partial Mixed Adaptive-Random Measurements
A novel framework to construct an efficient sensing (measurement) matrix,
called mixed adaptive-random (MAR) matrix, is introduced for directly acquiring
a compressed image representation. The mixed sampling (sensing) procedure
hybridizes adaptive edge measurements extracted from a low-resolution image
with uniform random measurements predefined for the high-resolution image to be
recovered. The mixed sensing matrix seamlessly captures important information
of an image, and meanwhile approximately satisfies the restricted isometry
property. To recover the high-resolution image from MAR measurements, the total
variation algorithm based on the compressive sensing theory is employed for
solving the Lagrangian regularization problem. Both peak signal-to-noise ratio
and structural similarity results demonstrate the MAR sensing framework shows
much better recovery performance than the completely random sensing one. The
work is particularly helpful for high-performance and lost-cost data
acquisition.Comment: 16 pages, 8 figure
Improving A*OMP: Theoretical and Empirical Analyses With a Novel Dynamic Cost Model
Best-first search has been recently utilized for compressed sensing (CS) by
the A* orthogonal matching pursuit (A*OMP) algorithm. In this work, we
concentrate on theoretical and empirical analyses of A*OMP. We present a
restricted isometry property (RIP) based general condition for exact recovery
of sparse signals via A*OMP. In addition, we develop online guarantees which
promise improved recovery performance with the residue-based termination
instead of the sparsity-based one. We demonstrate the recovery capabilities of
A*OMP with extensive recovery simulations using the adaptive-multiplicative
(AMul) cost model, which effectively compensates for the path length
differences in the search tree. The presented results, involving phase
transitions for different nonzero element distributions as well as recovery
rates and average error, reveal not only the superior recovery accuracy of
A*OMP, but also the improvements with the residue-based termination and the
AMul cost model. Comparison of the run times indicate the speed up by the AMul
cost model. We also demonstrate a hybrid of OMP and A?OMP to accelerate the
search further. Finally, we run A*OMP on a sparse image to illustrate its
recovery performance for more realistic coefcient distributions
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