Block Hadamard measurement matrix with arbitrary dimension in compressed sensing

Shaoqiang Liu; Xiaoyan Yan; Xiaoping Fan; Fei Li; Wen Xu

doi:10.1117/12.2265234

23 January 2017 Block Hadamard measurement matrix with arbitrary dimension in compressed sensing

Shaoqiang Liu, Xiaoyan Yan, Xiaoping Fan, Fei Li, Wen Xu

Proceedings Volume 10322, Seventh International Conference on Electronics and Information Engineering; 1032230 (2017) https://doi.org/10.1117/12.2265234
Event: Seventh International Conference on Electronics and Information Engineering, 2016, Nanjing, China

Abstract

As Hadamard measurement matrix cannot be used for compressing signals with dimension of a non-integral power-of-2, this paper proposes a construction method of block Hadamard measurement matrix with arbitrary dimension. According to the dimension N of signals to be measured, firstly, construct a set of Hadamard sub matrixes with different dimensions and make the sum of these dimensions equals to N. Then, arrange the Hadamard sub matrixes in a certain order to form a block diagonal matrix. Finally, take the former M rows of the block diagonal matrix as the measurement matrix. The proposed measurement matrix which retains the orthogonality of Hadamard matrix and sparsity of block diagonal matrix has highly sparse structure, simple hardware implements and general applicability. Simulation results show that the performance of our measurement matrix is better than Gaussian matrix, Logistic chaotic matrix, and Toeplitz matrix.

Citation Download Citation

Shaoqiang Liu, Xiaoyan Yan, Xiaoping Fan, Fei Li, and Wen Xu "Block Hadamard measurement matrix with arbitrary dimension in compressed sensing", Proc. SPIE 10322, Seventh International Conference on Electronics and Information Engineering, 1032230 (23 January 2017); https://doi.org/10.1117/12.2265234

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