Construction of Convolution Compressed Sensing Measurement Matrices Based on Cyclotomic Classes

Convolutional compressed sensing emerging in recent years is a new type of compressed sensing technology. By using cyclic matrix as measurement matrices, the sampling in convolutional compressed sensing can be simplified into convolution process, thus the complexity of the algorithm is greatly reduced. In this paper, a construction of measurement matrices for convolutional compressed sensing based on cyclotomic classes is proposed. The measurements are obtained by using the circulate convolution signal of the deterministic sequence and then by random subsampling. The correlation of the measurement matrix constructed in this paper is smaller than that of the existing constructions in the literature. The simulation results show that the measurement matrix constructed in this paper can recover the sparse signal better than the random Gaussian matrix under the same conditions. The proposed matrix can also be applied to channel estimation and reconstruction of two-dimensional images.