Optimal quantization by matrix searching
Journal of Algorithms
Vector quantization and signal compression
Vector quantization and signal compression
Pattern matching algorithms
Computing a minimum-weight k-link path in graphs with the concave Monge property
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Fixed-rate successively refinable scalar quantizers
DCC '96 Proceedings of the Conference on Data Compression
Entropy-Constrained Successively Refinable Scaler Quantization
DCC '97 Proceedings of the Conference on Data Compression
Practical Multi-Resolution Source Coding: TSVQ
DCC '98 Proceedings of the Conference on Data Compression
Quantization as Histogram Segmentation: Globally Optimal Scalar Quantizer Design in Network Systems
DCC '02 Proceedings of the Data Compression Conference
On Optimal Multi-resolution Scalar Quantization
DCC '02 Proceedings of the Data Compression Conference
Codecell Contiguity in Optimal Fixed-Rate and Entropy-Constrained Network Scalar Quantizers
DCC '02 Proceedings of the Data Compression Conference
On the structure of optimal entropy-constrained scalar quantizers
IEEE Transactions on Information Theory
On properties of locally optimal multiple description scalar quantizers with convex cells
IEEE Transactions on Information Theory
On L∞ properties of multiresolution scalar quantizers
IEEE Transactions on Information Theory
IEEE Transactions on Communications
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Multi-resolution quantization is a way of constructing a progressively refinable description of a discrete random variable. The underlying discrete optimization problem is to minimize an expected distortion over all refinement levels weighted by the probability or importance of the descriptions of different resolutions. This research is motivated by the application of multimedia communications via variable-rate channels. We propose an O(rN2) time and O(N2 log N) space algorithm to design a minimum-distortion quantizer of r levels for a random variable drawn from an alphabet of size N. It is shown that for a very large class of distortion measures the objective function of optimal multi-resolution quantization satisfies the convex Monge property. The efficiency of the proposed algorithm hinges on the convex Monge property. But our algorithm is simpler (even though of the same asymptotic complexity) than the well-known SMAWK fast matrix search technique, which is the best existing solution to the quantization problem. For exponential random variables our approach leads to a solution of even lower complexity: O(rN) time and O(N log N) space, which outperforms all the known algorithms for optimal quantization in both multi- and single-resolution cases. We also generalize the multi-resolution quantization problem to a graph problem, for which our algorithm offers an efficient solution.