Since the term compressive sensing was coined a few years ago [53, 100] this subject has been under intensive investigation [24, 56, 70]. It has found broad application in imaging, data compression, radar, and data acquisition to name a few. Overviews on compressive sensing can be found in, e.g., [56, 70]. Extensive references and resources on compressive sensing are also available online [1].

In a nutshell, compressive sensing is a novel paradigm where a signal that is sparse in a known transform domain can be acquired with much fewer samples than usually required by the dimensions of this domain. The only condition is that the sampling process is *incoherent* with the transform that achieves the sparse representation and *sparse* means that most weighting coefficients of the signal representation in the transform domain are zero. While it is obvious that a signal that is sparse in a certain basis can be fully represented by an index specifying the basis vectors corresponding to nonzero weighting coefficients plus the coefficients—determining *which* coefficients are nonzero would usually involve calculating all coefficients, which requires at least as many samples as there are basis functions. The definition of *incoherence* usually states that distances between sparse signals are approximately conserved as distances between their respective measurements generated by the sampling process. In this sense the reconstruction problem has per definition a unique ...

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