Theoretical foundations of transform coding

By Vivek K Goyal. 2001

439 citations recorded by the source corpus.

Discusses various aspects of transform coding, including: source coding, constrained source coding, the standard theoretical model for transform coding, entropy codes, Huffman codes, quantizers, uniform quantization, bit allocation, optimal transforms, transforms visualization, partition cell shapes, autoregressive sources, transform optimization, synthesis transform optimization, orthogonality and independence, and departures form the standard model.

Subfields: Computer Vision and Pattern Recognition, Signal Processing

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In Signal Processing

Citations in the corpus

End-to-end optimization of nonlinear transform codes for perceptual quality (2016, background): “Transform coding [1] is one of the most successful areas of signal processing.”
ELIC: Efficient Learned Image Compression with Unevenly Grouped Space-Channel Contextual Adaptive Coding (2022, positive): “As learned image compression is formulated as a sort of nonlinear transform coding [3,21], another plot improving coding performance is the development of main transform.”
Multiple description coding: compression meets the network (2001, background): “However, there are a few basic components that appear in many practical techniques, like prediction, quantization, decorrelating transforms, and entropy coding [34].”
Foundations of Signal Processing (2014, neutral): “Transform coding The review by Goyal [36] provides detailed coverage of transform coding, including a description of settings where a Karhunen–Loève transform is not optimal.”
Transform Coding Techniques for Lossy Hyperspectral Data Compression (2007, background): “This yields [23] that the optimal average distortion for a Gaussian source is D = γ( ∏N i=1 σi) 1 N 2−2R, with γ a given constant.”
Variational image compression with a scale hyperprior (2018, methodology): “In the transform coding approach to image compression (Goyal, 2001), the encoder transforms the image vector x using a parametric analysis transform g a ( x ; φ g ) into a latent representation y , which is then quantized to form ˆ y .”
A tutorial on modern lossy wavelet image compression: foundations of JPEG 2000 (2001, methodology): “The material in this section builds on the background material in generic transform coding given in [6] (further background in data compression can be found in [7]-[10]).”
The JPEG 2000 still image compression standard (2001, methodology): “Core Processing Wavelet Transform Wavelet transform is used for the analysis of the tile components into different decomposition levels [9], [26], [70], [71].”
Joint Autoregressive and Hierarchical Priors for Learned Image Compression (2018, methodology): “Most recent methods for learning-based, lossy image compression adopt an approach based on transform coding [1].”
The student-t mixture as a natural image patch prior with application to image compression (2014, methodology): “Most commonplace image compression schemes follow three main steps: transformation, quantization and entropy coding (Goyal, 2001).”
Information Bottleneck for Gaussian Variables (2003, background): “Since only few bits can be transmitted, the information has to be compressed in a relevant way, and the relative scaling of the different eigenvectors becomes important (as in transform coding Goyal, 2001).”
Variable Rate Deep Image Compression With a Conditional Autoencoder (2019, methodology): “Transform coding [8] has been successful to yield practical and efficient image compression algorithms such as JPEG [27] and JPEG2000 [18].”
Checkerboard Context Model for Efficient Learned Image Compression (2021, methodology): “The common key of those currently most successful approaches is the entropy modeling and optimizing method, with autoencoder based structure to perform a nonlinear transform coding [14, 5].”
Error correction via linear programming (2005, background): “Theorem 3.7 (Euclidean projections of the cube [28]).”