Laurent Jacques examines the potential ability for SPGL1 to perform TV minimization in a blog entry entitled SPGL1 and TV minimization ?, if you have some thoughts on the matter, please share them with him.
In a different area when one is looking for an answer on what type of dictionary of *lets to use, here an investigation entitled A hitchhiker’s guide to the galaxy of transform-domain sparsification by Evgeniy Lebed and Felix Herrmann. The abstract reads:
The ability to efficiently and sparsely represent seismic data is becoming an increasingly important problem in geophysics. Over the last decade many transforms such as wavelets, curvelets, contourlets, surfacelets, shearlets, and many other types of 'x-lets' have been developed to try to resolve this issue. In this abstract we compare the properties of four of these commonly used transforms, namely the shift-invariant wavelets, complex wavelets, curvelets and surfacelets. We also briefly explore the performance of these transforms for the problem of recovering seismic wavefields from incomplete measurements.
From I am no geek blog, I found: Combining Compressed Sensing and Parallel Imaging by K. F. King. The introduction reads:
Compressed sensing and parallel imaging use fundamentally different acceleration methods. Compressed sensing relies on L1-norm minimization in a sparse transform space to allow reconstruction of randomly undersampled k-space data (1). Parallel imaging uses L2-norm error minimization to incorporate receive B1 information into the reconstruction of undersampled multicoil k-space data (2). An L1-norm penalty function has also been used in image denoising (3) and to denoise and regularize parallel imaging and non-Cartesian k-space reconstructions (4). It is desirable to combine these techniques for improved acceleration and robustness.
Credit: NASA/JPL/Space Science Institute, Great Southern Land
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