Fewer Bernoulli Measurements Satisfying the Constraint of Reconstruction Probability

In the compressed sensing (CS) framework, the previous methods statistically provide the probability of signal reconstruction when the number of measurements is given. However, when the reconstruction probability of the signal is constrained, these existing methods do not provide an effective mechanism to find the measurements satisfying the constraint. To handle the problem, we focus on Bernoulli measurements and utilize the reconstruction feature of Bernoulli measurements and sequential CS to determine the measurements such that they can satisfy the constraint of reconstruction probability. Moreover, the measurements obtained by the proposed method are fewer than those by the classical methods because some redundant measurements are removed from the obtained measurement sequence. In summary, the proposed method has three unique features: satisfying the constraint of reconstruction probability, containing fewer measurements, and having the property of global convergence. Both theoretical analysis and experimental results suggest that the proposed method can obtain fewer measurements which satisfy the required reconstruction probability for different sparse signals and different initial measurements.