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Optimal compressive imaging for Fourier data
Published on Oct 29, 20142860 Views
One fundamental problem in applied mathematics is the issue of recovery of data from speci c samples. Of particular importance is the case of pointwise samples of the associated Fourier transform, w
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Chapter list
Optimal Compressive Imaging for Fourier Data00:00
Untitled00:06
Sensing Data01:12
Fourier Sampling02:27
General Sampling Strategy using Sparsity04:18
Compressed Sensing Type Approaches07:10
Appropriate Notion of Optimality?07:45
Looking ahead...09:58
Let’s start with a suitable Model...10:55
Anisotropic/Cartoon Structures11:05
Sparsifying Representation System13:14
Compactly Supported Shearlets14:41
Problem with Frames16:04
Dualizable Shearlets...17:21
Intuition: Partition of Fourier Domain, shear= 017:25
Intuition: Partition of Fourier Domain, shear6= 017:29
Intuition: Filters17:31
Shearlet Generators17:51
Dualizable Shearlet Frame18:43
Optimal Sparse Approximation inherited!19:55
Directional Sampling Strategy20:00
Sampling Strategy: Dualizable Shearlet Systems20:11
Shear-Adapted Density Sampling22:45
Sparse Sampling Strategy23:27
Numerical Experiments26:12
Sampling Schemes26:14
Numerical Results for 512x512 MRI Image26:29
Approximation Curves for 512x512 MRI Image27:02
Let’s conclude...28:29
What to take Home...?28:32
THANK YOU!29:23