Vector quantization using LBG method of center splitting

资 源 简 介

Vector quantization using LBG method of center splitting

详 情 说 明

Vector quantization is a technique widely used in data compression and signal processing to reduce the complexity of high-dimensional data. The Linde-Buzo-Gray (LBG) algorithm is a popular method for designing a codebook that efficiently represents the input data vectors. One of the key approaches in LBG is center splitting, which helps in refining the codebook iteratively.

The LBG algorithm starts with an initial codebook, often just the centroid of the entire dataset. The center splitting technique is then applied to generate a more refined set of codewords. The process involves:

Initialization – Starting with a single centroid representing the entire dataset. Splitting – Each existing centroid is perturbed (split into two) by adding and subtracting a small distortion, effectively doubling the number of codewords. Clustering – The input vectors are reassigned to the nearest new codewords using a distance metric (e.g., Euclidean distance). Centroid Update – The codewords are recalculated as the mean of all vectors assigned to them. Iteration – Steps 2-4 are repeated until the desired number of codewords is reached or the distortion falls below a threshold.

This method ensures that the final codebook closely approximates the distribution of the original data while minimizing quantization error. Center splitting is particularly efficient in scenarios like speech and image compression, where reducing data dimensionality without significant loss of information is crucial.

The LBG algorithm's strength lies in its simplicity and convergence properties, making it a foundational method in vector quantization. However, variations and optimizations (such as tree-structured search) are often employed to improve computational efficiency for large datasets.