Recovery performance improvement of image compressive sensing using complex‐valued Vandermonde matrix

Abstract

Abstract Here, a novel image‐based quantized compressive sensing (QCS) framework based on complex‐valued Vandermonde (Vander) matrix is proposed. In the proposed QCS framework, a discrete wavelet transform (DWT) serves as a sparse basis and a partial complex‐valued Vander matrix serves as a measurement matrix. The theoretical analysis based on mutual coherence metric of compressive sensing (CS) theory shows that the proposed Vander measurement matrix has the best reconstruction performance among other conventional measurement matrices. The simulation results also show that the recovery quality using the proposed measurement matrix can be greatly improved compared with the other existing real‐valued measurement matrices. In particular, the experiment results also show that under the same measurement matrix, the reconstruction performance of Smoothed l0 norm (SL0) algorithm is better than that of Orthogonal Matching Pursuit (OMP) algorithm, sparsity adaptive matching pursuit (SAMP) algorithm and approximate message passing (AMP) algorithm. In addition, a sparse measurement matrix scheme is further proposed to achieve a trade‐off between recovery performance and computational complexity. The theoretical analysis and simulation results both show the proposed image‐based QCS is efficient.

Keywords

• compressed sensing
• image reconstruction
• Vandermonde matrix