Quantum mechanics

Nonlinear distortion

Vector quantization

Video tracking

Algorithm

Rate distortion

Quantization (signal processing)

Bandwidth (computing)

Statistics

Rate–distortion optimization

Multiview Video Coding

Entropy (arrow of time)

Rate–distortion theory

Telecommunications

Distortion (music)

Coding (social sciences)

Amplifier

Computer science

Mathematical optimization

Codec

Physics

Nonlinear system

Discrete cosine transform

Pattern recognition (psychology)

Mathematics

Image (mathematics)

Object (grammar)

Artificial intelligence

Data compression

Transform coding

IEEE Journal of Selected Topics in Signal Processing

We review a class of methods that can be collected under the name nonlinear transform coding (NTC), which over the past few years have become competitive with the best linear transform codecs for images, and have superseded them in terms of rate-distortion performance under established perceptual quality metrics such as MS-SSIM. We assess the empirical rate-distortion performance of NTC with the help of simple example sources, for which the optimal performance of a vector quantizer is easier to estimate than with natural data sources. To this end, we introduce a novel variant of entropy-constrained vector quantization. We provide an analysis of various forms of stochastic optimization techniques for NTC models; review architectures of transforms based on artificial neural networks, as well as learned entropy models; and provide a direct comparison of a number of methods to parameterize the rate-distortion trade-off of nonlinear transforms, introducing a simplified one.

Nonlinear Transform Coding