Geodesic
Optimization of Frame Representations for Compressed Sensing and Mercedes-Benz Frame
Trudy Matematicheskogo Instituta imeni V.A. Steklova, 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. 
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S. Ya. Novikov; I. S. Ryabtsov. Optimization of Frame Representations for Compressed Sensing and Mercedes-Benz Frame. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected topics of mathematical physics and $p$-adic analysis, Tome 265 (2009), pp. 211-219. http://geodesic.mathdoc.fr/item/TM_2009_265_a17/

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