<title>Optimized vector quantization with fuzzy distortion measure</title>

Abstract

From the perspective of information theory, the design of vector quantizers (VQs) in optimizing the rate distortion function has been extensively studied. In practice, however, the existing VQ algorithms, often, suffer from a number of serious problems, e.g., long search process, codebook initialization, and getting trapped in local minima, inherent to most iterative processes. The generalized Lloyd algorithm, for designing VQs with embedded k-means clustering for codebook generation has been recently used by a number of researcher for efficient image coding by quantizing wavelet decomposed subimages. We present a new approach to vector quantization by generating such multiresolution codebooks using two different neuro-fuzzy clustering techniques that eliminate the existing problems. These clustering techniques integrate fuzzy optimization constraints from the fuzzy-C-means with self-organizing neural network architectures. In one of the new clustering techniques, a new distance measure has also been introduced. The resulting multiresolution codebooks generated from the wavelet decomposed images yield significant improvement in the coding process. The signal transformation and vector quantization stages together yield, at least, 64:1 bit rate reduction with good visual quality and acceptable peak signal to noise ratio (PSNR) and mean square error (MSE). Additional bit rate reduction can be easily obtained by employing conventional entropy encoding after the quantization stage. The performance of this new VQ coding technique has been compared to that of the well-known Linde, Buzo, and Gray (LBG) - VQ for a variety of image classes. The new VQ technique demonstrated superior ability for fast convergence with minimum distortion at similar bit rate reduction then the existing VQ technique for several classes of images/signals including standard test images and medical images in terms of mean-squared error (MSE), peak-signal-to- noise-ratio (PSNR), and visual quality.