Zigzag Ordered Walsh Matrix for Compressed Sensing Image Sensor

In compressed sensing (CS) based CMOS image sensors (CS-CIS), the ternary measurement matrix determines the compression performance in terms of decoded image quality versus sampling rate (data rate). Several studies have been carried out to investigate the effect of Hadamard and Walsh projection order selection on image reconstruction quality by simply reordering orthogonal matrices [1]. However, there is still room for improvement in the quality of reconstructed images from these works, especially at low SR. In this paper, we propose a structured measurement matrix called Zigzag ordered Walsh matrix (ZoW), which outperforms at low sampling rates. Firstly, the Walsh matrix is divided into several measurement patterns. Because the lower frequency component in an image plays a more critical role in determining the image quality, we arrange low-frequency patterns on the upper-left corner, and the frequency increases according to the zigzag scan order. Then, vectorize each pattern and stacking back into ZoW matrix. Hence, under various sampling rates, the proposed ZoW always remains the lowest frequency patterns which are the most critical patterns. Comparing with the existing measurement matrices, recovery errors are improved by 4.09dB in PSNR on average and provided significantly better image quality via visual perception when sampling rates are 5%~15%.In Table 1, we can observe that the reconstruction quality via PSNR is improved by 4.63dB, and SSIM is improved 69% on average when the sampling rate is 10%.