Chen Qunlin, Chen Derong, Gong Jiulu, Ruan Jie
School of Mechatronical Engineering, Beijing Institute of Technology, Beijing 100081, China.
Entropy (Basel). 2020 Jan 20;22(1):125. doi: 10.3390/e22010125.
Compressed sensing (CS) offers a framework for image acquisition, which has excellent potential in image sampling and compression applications due to the sub-Nyquist sampling rate and low complexity. In engineering practices, the resulting CS samples are quantized by finite bits for transmission. In circumstances where the bit budget for image transmission is constrained, knowing how to choose the sampling rate and the number of bits per measurement (bit-depth) is essential for the quality of CS reconstruction. In this paper, we first present a bit-rate model that considers the compression performance of CS, quantification, and entropy coder. The bit-rate model reveals the relationship between bit rate, sampling rate, and bit-depth. Then, we propose a relative peak signal-to-noise ratio (PSNR) model for evaluating distortion, which reveals the relationship between relative PSNR, sampling rate, and bit-depth. Finally, the optimal sampling rate and bit-depth are determined based on the rate-distortion (RD) criteria with the bit-rate model and the relative PSNR model. The experimental results show that the actual bit rate obtained by the optimized sampling rate and bit-depth is very close to the target bit rate. Compared with the traditional CS coding method with a fixed sampling rate, the proposed method provides better rate-distortion performance, and the additional calculation amount amounts to less than 1%.
压缩感知（CS）提供了一种图像采集框架，由于其亚奈奎斯特采样率和低复杂度，在图像采样和压缩应用中具有出色的潜力。在工程实践中，生成的CS样本通过有限位进行量化以便传输。在图像传输的比特预算受限的情况下，了解如何选择采样率和每次测量的比特数（比特深度）对于CS重建的质量至关重要。在本文中，我们首先提出一种考虑CS压缩性能、量化和熵编码器的比特率模型。该比特率模型揭示了比特率、采样率和比特深度之间的关系。然后，我们提出一种用于评估失真的相对峰值信噪比（PSNR）模型，该模型揭示了相对PSNR、采样率和比特深度之间的关系。最后，基于比特率模型和相对PSNR模型，根据率失真（RD）准则确定最佳采样率和比特深度。实验结果表明，通过优化的采样率和比特深度获得的实际比特率非常接近目标比特率。与具有固定采样率的传统CS编码方法相比，所提出的方法提供了更好的率失真性能，并且额外的计算量不到1%。
