Mathematics Colloquia and Seminars
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Grid independent compressive imagingStudent-Run Applied & Math Seminar
|Speaker: ||Wenjing Liao, University of California, Davis|
|Location: ||2112 MSB|
|Start time: ||Fri, Jan 25 2013, 12:10PM|
In the process of discretizing continuum imaging problems,a gridding
error,roughly proportional to the grid spacing, arises. When the grid
spacing is above the Rayleigh length, the gridding error can be as large as
the data themselves, creating an unfavorable signal to noise ratio. To
reduce the gridding error, it’s natural to refine the grid. However, the
sensing matrices become underdetermined and highly coherent when the grid
spacing is reduced below the Rayleigh length. In this case, existing
compressive sensing(CS) algorithms fail due to the absence of incoherence.
In order to fill the gap, we propose the techniques of band exclusion(BE)
and local optimization(LO) to deal with coherent sensing matrices on fine
grid. These techniques are embedded in the existing CS algorithms, such as
Orthogonal Matching Pursuit(OMP) and Basis Pursuit(BP), and result in the
modified algorithms, such as BLO-based OMP and BLO-based BP respectively.
We have proved that under certain conditions, BLO-based OMP is capable of
reconstructing sparse, widely separated objects within one Rayleigh length
in bottleneck distance independent of the grid spacing.Detailed numerical
comparisons with other algorithms designed for the same purpose, such as
Spectral Iterative Hard Thresholding(SIHT) and the analysis-based BP,
demonstrate the superiority of BLO-based OMP and BLO-based BP.
Pizzas and sodas will be provided.