满足重构概率约束的更少贝努利观测

在压缩感知(Compressed sensing, CS)中,一些方法统计地提供了给定观测数量下的信号重构概率. 然而,在重构概率有约束的情况下,现有方法不能找到满足约束的观测. 本文以压缩感知中常用的贝努利观测集为研究对象, 基于贝努利观测的特征和序列压缩感知理论获得了满足重构概率约束的观测. 另外,由于所提方法能从获取的过多观测中移除部分冗余观测, 观测结果包含更少的观测数据. 所提方法有三个优点:满足重构概率约束、 包含更少的观测数据以及具有全局收敛的属性. 理论分析和实验结果验证了所提方法的有效性.

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.