Sparse DP Quantization Algorithm

Abstract

We formulate the design of an optimal quantizer as an optimization problem that finds the quantization indices that minimize quantization error. As a solution of the optimization problem, an approach based on dynamic programming, which is called DP quantization, is proposed. It is observed that quantized signals do not always contain all kinds of signal values which can be represented with given bit-depth. This property is called amplitude sparseness. Because quantization is the amplitude discretization of signal value, amplitude sparseness is closely related to quantizer design. Signal values with zero frequency do not impact quantization error, so there is the potential to reduce the complexity of the optimal quantizer by not computing signal values that have zero frequency. However, conventional methods for DP quantization were not designed to consider amplitude sparseness, and so fail to reduce complexity. The proposed algorithm offers a reduced complexity optimal quantizer that minimizes quantization error while addressing amplitude sparseness. Experimental results show that the proposed algorithm can achieve complexity reduction over conventional DP quantization by 82.9 to 84.2% on average.

Multi-Layered DP Quantization Algorithm

“…Specifically, the analytical models do not consider the complexity reduction achieved by restricting the search range, see Sect. 5.2 in [17].…”

“…The proposed algorithm leads to computation efficiency while keeping the optimality of multi-level quantization in terms of minimizing the total amount of quantization error. Furthermore, our layered approach can be incorporated into sparse DP quantization (SDP-Q) [17] in the same way as DP quantization. Figure 6 shows the running time of our layered approach built on SDP-Q (abbreviated as LySDP-Q) and the simultaneous approach built on SDP-Q (abbreviated as SmSDP-Q).…”

“…In the following, feasible paths within the search range are abbreviated as candidate paths, and candidate paths that are shared between both quantizations are abbreviated as shared candidate paths. According to [17], the number of candidate paths for DP-Q that quantizes a K-level signal into a M-level signal is derived as follows:…”

“…The complexity of "C2" is related to the number of candidate intervals in the input histogram, because the quantization error of each candidate interval needs to be computed and stored in E[]. According to [17], the number of candidate intervals for DP-Q that quantizes a K-level signal into a M-level signal is derived as follows:…”

“…For designing optimal quantizers, adaptive quantization algorithms based on dynamic programming (DP quantization), which originated in Bruce's algorithm [14], have been studied. For example, so as to reduce the complexity of DP quantization, Sharma [15] attempts to minimize the quantization error subject to a convexity constraint, Wu [16] uses matrix search to find optimal solutions for DP quantization, and Bandoh [17] focuses on the amplitude sparseness of signal values. Some applications for HDR images such as SDR display adaptation and bit-depth scalable coding need to convert a source signal with high bit-depth into multiple formats with lower bit-depths to support a wide variety of user environments.…”