Compressed sensing and the synthesis formulation
Résumé
There is clear empirical evidence that the use of redundant dictionaries instead of orthogonal bases can significantly improve the recovery results in compressed sensing. The theoretical understanding of this phenomenon is however still partial. The objective of this work is to better understand the so-called synthesis formulation in the framework of random Gaussian measurements. We derive new sharp guarantees for robust recovery of coefficient representations and of signals using the machinery of conic Gaussian widths.
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