PREFACE

The reason why this question is important is that compressed-sensing (CS) has been intensely discussed in the engineering community for more than a decade as a hot research topic, gathering a great deal of effort from a large community that unites scientists in applied mathematics and information theory, as well as engineers of analog/digital circuits and optical systems. Yet, several investigations have been dominated by a few misconceptions that somehow hindered the application of this promising technique to real-world systems. The first concept is that optimization and adaptivity are fundamentally pointless since CS is born as a universal technique that cannot be significantly improved. The second is that even if one wants to optimize CS, the degrees of freedom to do it are not there, since it is a technique that spreads information so uniformly that no criteria are able to tell important parts to emphasize from less important parts to neglect. Both concepts are grounded in fundamental mathematical results that are indeed the pillars of CS and are indispensable pieces of the formal construction on which the whole discipline relies. Regrettably, starting from formally true theorems, the folklore has sometimes derived misleading design guidelines. The idea that adaptivity is useless, often indicated as universality, has its roots in the seminal papers originating the very concept of CS and in other later informationtheoretic results. In the original setting, such an idea is extremely important to put CS in the right perspective and give it the full dignity of an acquisition method with general applicability. The mathematical derivations produce upper bounds on the ratio between the performance of an adaptive strategy with respect to that of nonadaptive CS. Such bounds being finite, we know that the performance of an agnostic CS is not too far away for the most specialized technique one may devise. Yet, in