The JPEG still picture compression standard
Communications of the ACM - Special issue on digital multimedia systems
Vector quantization and signal compression
Vector quantization and signal compression
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
IEEE Transactions on Information Theory
Transform coding with backward adaptive updates
IEEE Transactions on Information Theory
Weighted universal image compression
IEEE Transactions on Image Processing
Optimally adaptive transform coding
IEEE Transactions on Image Processing
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Abstract: We propose a new transform coding algorithm that integrates all optimization steps in to a coherent and consistent framework. Each iteration of the algorithm is designed to minimize coding distortion as a function of both the transform and quantizer designs. Our algorithm is a constrained version of the LBG algorithm for vector quantizer design. The reproduction vectors are constrained to lie at the vertices of a rectangular grid. A significant result of our approach is a new transform basis specifically designed to minimize mean-squared quantization distortion for both fixed-rate and entropy-constrained coding. For Gaussian distributed data, this transform reduces to the Karhunen-Loeve transform (KLT). However, in general the coding optimal transform (COT) differs from the KLT enough to provide up to 1 dB improvement in compressed signal-to-noise ratio (SNR) on images. We describe a practical algorithm that finds the COT for a given signal. In addition, we present image compression results demonstrating the SNR improvement achieved with our algorithm relative to KLT based transform coding.