Variable-length constrained-storage tree-structured vector quantization

Abstract

Constrained storage vector quantization, (CSVQ), introduced by Chan and Gersho (1990, 1991) allows for the stagewise design of balanced tree-structured residual vector quantization codebooks with low encoding and storage complexities. On the other hand, it has been established by Makhoul et al. (1985), Riskin et al. (1991), and by Mahesh et al. (see IEEE Trans. Inform. Theory, vol.41, p.917-30, 1995) that variable-length tree-structured vector quantizer (VLTSVQ) yields better coding performance than a balanced tree-structured vector quantizer and may even outperform a full-search vector quantizer due to the nonuniform distribution of rate among the subsets of its input space. The variable-length constrained storage tree-structured vector quantization (VLCS-TSVQ) algorithm presented in this paper utilizes the codebook sharing by multiple vector sources concept as in CSVQ to greedily grow an unbalanced tree structured residual vector quantizer with constrained storage. It is demonstrated by simulations on test sets from various synthetic one dimensional (1-D) sources and real-world images that the performance of VLCS-TSVQ, whose codebook storage complexity varies linearly with rate, can come very close to the performance of greedy growth VLTSVQ of Riskin et al. and Mahesh et al. The dramatically reduced size of the overall codebook allows the transmission of the code vector probabilities as side information for source adaptive entropy coding.

A fast vector quantization encoding algorithm based on projection pyramid with Hadamard transformation

“…(1), the computational cost of finding the best suitable codevector in encoding and codebook design imposes practical limits on the codebook size N and the vector dimension k. When N and/or k become larger, the computation complexity problem occurs for full codebook search. Researchers have proposed numerous fast search approaches to speed up codebook matching process, including standard VQ, tree structure VQ (TSVQ) [3,[23][24][25], and lattice VQ (LVQ) [2,19,22,32]. The standard VQ algorithms can be classified into three classes.…”

Efficient binary search space‐structured VQ encoder applied to a line spectral frequency quantisation in G.729 standard

“…Conventionally, VQ conducts a full search to ensure a codeword best matched with an arbitrary input vector, but a full search requires an enormous computational load. Thus, as in a great volume of published studies [7][8][9][10][11][12][13][14][15][16], a continuous effort has been made to simplify the search complexity of an encoding process. These approaches are further classified into two types in terms of the way the complexity is simplified.…”

“…These approaches are further classified into two types in terms of the way the complexity is simplified. One is the tree-structured VQ (TSVQ) techniques [7][8][9][10][11][12] and the other is the triangular inequality elimination (TIE) based approaches [13][14][15][16].…”

<title>Performance analysis of tabular nearest-neighbor encoding for joint image compression and ATR: I. Background and theory</title>

“…Implementationally, two additional issues arise in VQ-based compression. First, derivation of a representative set ofpattems to form a compact codebook has been an elusive goal of VQ research for several decades [14][15][16]. Second, given a representative codebook of Q exemplars and a source image of N pixels subdivided into a collection of K-pixel neighborhoods, the codebook search overhead involved in matching source patterns to codebook patterns approaches a minimum of NQ comparisons for Boolean images and 2NQ additions for greyscale imagery [17].…”