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This paper proposed and constructed a new class of deterministic measurements matrix by using decimated binary Legendre sequences for convolutional Compressed Sensing. The author proves that when the measurement matrix is constructed by a random subsampling, it can offer a stable sparse reconstruction. Besides, the simulation results shows that when a deterministic subsampler is used, the proposed matrix can also guarantee the stable reconstruction as good as random Gaussian or Bernoulli matrixes do, which are commonly used in CS

Construction of Deterministic Measurements Matrix Using Decimated Legendre Sequences