Abstract
In compressed sensing, the sampling rate can be greatly reduced based on the sparsity of the original signal; however, quantisation is one key aspect in signal acquirement. This article studies the scalar quantisation and its impacts on the compressed sensing. We consider the case in which both the original and the measurement signals are quantised or discrete, which widely exists in the practical applications such as the finite precision signals in the computer and the finite-set original signal in communication systems. We derive the recovery probability bound and the necessary measurement number bound for compressed sensing with scalar quantisation and simulate three modified compressed sensing recovery algorithms. Simulations show that coarse quantisation can be applied in compressed sensing for discrete or quantised sparse signal with sampling and storage efficiency.
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