Nonuniform quantization for block-based compressed sensing of images in differential pulse-code modulation framework

In practical signal processing, it is necessary to quantize the sampled signals. Quantization is considered a necessary step to digitalize signals and realize the high-efficient transmission of digital signals. As a new signal processing theory, compressed sensing (CS) which is promoted as a joint sampling and compression approach for sparse signals has caused wide public concern in the field of image processing. In a practical application, although quantization is unavoidable for CS measurements, CS literature has largely avoided to discuss the topic of quantization. In this paper, differential pulse-code modulation(DPCM) is coupled with nonuniform scalar quantization(nonuniform SQ) to provide block-based compressed sensing (BCS) quantization of images. This paper analyzes the distribution of prediction errors in DPCM framework and draws a conclusion that in statistical sense such distribution is consistent with the characteristics of nonuniform scalar quantization. This discovery provides a theoretical basis for the proposed quantization method. Experimental results show that the proposed quantization scheme effectively increases the quantized signal to noise ratio(SNR), meanwhile improves the quality of reconstructed images.