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Research on the Relation between the Number of Measurements and Signal Sparsity in Compressed Sensing

Compressed sensing theory is a new theory which acquires, encodes and decodes sparse or appropriately sparse signals. The key issue in compressed sensing is to choose a suitable number of measurements which adapts to the signal sparsity. To get a more adaptive number of measurements, we choose random signals with different sparsities as experimental samples and modify the original relation between the number of measurements and signal sparsity. Compared with the original relation, the modified relation can ideally reconstruct the original signal with smaller measurements. Then we verify that the modified relation is not only applied to random signals but also has strong applicability to periodic signals.