Researching on wavelet BASIS for Compressive Sensing

From SeedWiki

Orthonormal QMF Filter for Wavelet Transform

Many image transformed domins are much more sparse than the original image itself. Wavelet is a very good one.

The orignial image	'haar' based wavelet coeffients

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The sparsity of the wavelet 'haar' BASIS

1% basis has been used to reconstruct	5% basis has been used to reconstruct	15% basis has been used to reconstruct	20% basis has been used to reconstruct

Note: This example is only for demostrating the sparsity of wavelet basis. Because in the CS framework, the K-largest coeffients are not measured directly.

But in this case, it is using M-largest coeffients to reconstruct.

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There is another way to construct better BASIS for CS based image reconstruction.

Check the paper K-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation.