A wonderful triangle in compressed sensing
Jun Wang

TL;DR
This paper introduces a geometric triangle involving $\, ext{l}_0$, $\, ext{l}_1$, and $\, ext{l}_ ext{infinity}$ norms to analyze sparse signal reconstruction, proposing a new sparsity-promoting objective and comparing different minimization algorithms.
Contribution
It presents a novel geometric framework called the wonderful triangle to relate different norms for sparse approximation and introduces a new sparsity interval and objective function.
Findings
The $\, ext{l}_1/ ext{l}_ ext{infinity}$ minimization is effective for sparse signals.
Comparison shows $\, ext{l}_1/ ext{l}_ ext{infinity}$ outperforms $\, ext{l}_1/ ext{l}_2$ in certain cases.
The geometric triangle provides insights into the relationships among norms in sparse recovery.
Abstract
In order to determine the sparse approximation function which has a direct metric relationship with the quasi-norm, we introduce a wonderful triangle whose sides are composed of , and for any non-zero vector by delving into the iterative soft-thresholding operator in this paper. Based on this triangle, we deduce the ratio and norms as a sparsity-promoting objective function for sparse signal reconstruction and also try to give the sparsity interval of the signal. Considering the minimization from a angle of the triangle corresponding to the side whose length is , we finally demonstrate the performance of…
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Taxonomy
TopicsSparse and Compressive Sensing Techniques · Photoacoustic and Ultrasonic Imaging · Ultrasound Imaging and Elastography
