Optimal entropy-constrained non-uniform scalar quantizer design for low bit-rate pixel domain DVC

In this paper, an optimal entropy-constrained non-uniform scalar quantizer is proposed for the pixel domain DVC. The uniform quantizer is efficient for the hybrid video coding since the residual signals conforming to a single-variance Laplacian distribution. However, the uniform quantizer is not optimal for pixel domain distributed video coding (DVC). This is because the uniform quantizer is not adaptive to the joint distribution of the source and the SI, especially for low level quantization. The signal distribution of pixel domain DVC conforms to the mixture model with multi-variance. The optimal non-uniform quantizer is designed according to the joint distribution, the error between the source and the SI can be decreased. As a result, the bit rate can be saved and the video quality won’t sacrifice too much. Accordingly, a better R-D trade-off can be achieved. First, the quantization level is fixed and the optimal RD trade-off is achieved by using a Lagrangian function J(Q). The rate and distortion components is designed based on P(Y|Q). The conditional probability density function of SI Y depend on quantization partitions Q, P(Y|Q), is approximated by a Guassian mixture model at encocder. Since the SI can not be accessed at encoder, an estimation of P(Y|Q) based on the distribution of the source is proposed. Next, J(Q) is optimized by an iterative Lloyd-Max algorithm with a novel quantization partition updating algorithm. To guarantee the convergence of J(Q), the monotonicity of the interval in which the endpoints of the quantizer lie must be satisfied. Then, a quantizer partition updating algorithm which considers the extreme points of the histogram of the source is proposed. Consequently, the entropy-constrained optimal non-uniform quantization partitions are derived and a better RD trade-off is achieved by applying them. Experiment results show that the proposed scheme can improve the performance by 0.5 dB averagely compared to the uniform scalar quantization.