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from Part Three - Compressive Sensing
Published online by Cambridge University Press: 21 April 2022
A Boolean analog of the standard compressive sensing problem, known as nonadaptive group testing, is analyzed in this chapter. Its success is characterized via the notion of separability (intimately related to disjunctiveness and strong selectivity) of the testing procedure. The minimal number of tests making separability possible is determined, and a deterministic procedure using roughly this number of tests is presented. Finally, it is shown that solving a linear feasibility program allows one to exactly recover sparse binary vectors from the outcomes of a separable testing procedure.
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