Geodesic
Optimization of Frame Representations for Compressed Sensing and Mercedes-Benz Frame
Informatics and Automation, Selected topics of mathematical physics and $p$-adic analysis, Tome 265 (2009), pp. 211-219

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We prove that there is no single uniform tight frame in Euclidean (unitary) space such that a solution of the $\ell_1$-norm minimization problem for the frame representation is attained on the frame coefficients. Then we find an exact solution of the $\ell_1$-minimization problem for the Mercedes-Benz frame in $\mathbb R^N$. We also give some examples of connections between optimization problems of various types. 
@article{TRSPY_2009_265_a17,
     author = {S. Ya. Novikov and I. S. Ryabtsov},
     title = {Optimization of {Frame} {Representations} for {Compressed} {Sensing} and {Mercedes-Benz} {Frame}},
     journal = {Informatics and Automation},
     pages = {211--219},
     publisher = {mathdoc},
     volume = {265},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2009_265_a17/}
}
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S. Ya. Novikov; I. S. Ryabtsov. Optimization of Frame Representations for Compressed Sensing and Mercedes-Benz Frame. Informatics and Automation, Selected topics of mathematical physics and $p$-adic analysis, Tome 265 (2009), pp. 211-219. http://geodesic.mathdoc.fr/item/TRSPY_2009_265_a17/