Image parallel block compressive sensing scheme using DFT measurement matrix

Compressive sensing (CS)-based image coding has been widely studied in the field of image processing. However, the CS-based image encoder has a significant gap in image reconstruction performance compared with the conventional image compression methods. In order to improve the reconstruction quality of CS-based image encoder, we proposed an image parallel block compressive sensing (BCS) coding scheme, which is based on discrete Cosine transform (DCT) sparse basis matrix and partial discrete Fourier transform (DFT) measurement matrix. In the proposed parallel BCS scheme, each column of an image block is sampled by the same DFT measurement matrix. Due to the complex property of DFT measurement matrix, the compressed image data is complex. Then, the real part and imaginary part of the resulting BCS data are quantized and transformed into two bit streams, respectively. At the reconstruction stage, the resulting two bit streams are transformed back into two real signals using inverse quantization operation. The resulting two real signals are combined into one complex signal, which is served as the input data of the CS reconstructed algorithm. The theoretical analysis based on minimum Frobenius norm method demonstrates that the proposed DFT measurement matrix outperforms the other conventional measurement matrices. The simulation results show that the reconstructed performance of the proposed DFT measurement matrix is better than that of the other conventional measurement matrices for the proposed parallel BCS. Specifically, we analyzed the impact of quantization on the reconstruction performance of CS. The experiment results show that the effect of the quantization on reconstruction performance in BCS framework can nearly be ignored.