Density Modeling of Images using a Generalized Normalization Transformation

Abstract

We introduce a parametric nonlinear transformation that is well-suited for Gaussianizing data from natural images. The data are linearly transformed, and each component is then normalized by a pooled activity measure, computed by exponentiating a weighted sum of rectified and exponentiated components and a constant. We optimize the parameters of the full transformation (linear transform, exponents, weights, constant) over a database of natural images, directly minimizing the negentropy of the responses. The optimized transformation substantially Gaussianizes the data, achieving a significantly smaller mutual information between transformed components than alternative methods including ICA and radial Gaussianization. The transformation is differentiable and can be efficiently inverted, and thus induces a density model on images. We show that samples of this model are visually similar to samples of natural image patches. We demonstrate the use of the model as a prior probability density that can be used to remove additive noise. Finally, we show that the transformation can be cascaded, with each layer optimized using the same Gaussianization objective, thus offering an unsupervised method of optimizing a deep network architecture.

published as a conference paper at ICLR 2016

Cited by in corpus (51)

• Conditional Image Synthesis With Auxiliary Classifier GANs
• End-to-end Optimized Image Compression
• Density estimation using Real NVP
• Wireless Image Transmission Using Deep Source Channel Coding With Attention Modules
• Video Coding for Machines: A Paradigm of Collaborative Compression and Intelligent Analytics
• Masked Autoregressive Flow for Density Estimation
• Causal Contextual Prediction for Learned Image Compression
• Scalable Image Coding for Humans and Machines
• Variable Rate Deep Image Compression with Modulated Autoencoder
• Joint Device-Edge Inference over Wireless Links with Pruning
• Roundtrip: A Deep Generative Neural Density Estimator
• Supervised Compression for Resource-Constrained Edge Computing Systems
• A Unified End-to-End Framework for Efficient Deep Image Compression
• Attention-based Convolutional Autoencoders for 3D-Variational Data Assimilation
• Towards Robust Neural Image Compression: Adversarial Attack and Model Finetuning
• End-to-End Learnable Multi-Scale Feature Compression for VCM
• Artifact- and content-specific quality assessment for MRI with image rulers
• Boosting Neural Image Compression for Machines Using Latent Space Masking
• Learned Video Compression via Heterogeneous Deformable Compensation Network
• Deep Perceptual Compression
• Transform Network Architectures for Deep Learning based End-to-End Image/Video Coding in Subsampled Color Spaces
• The Sparse Manifold Transform
• PerceptNet: A Human Visual System Inspired Neural Network for Estimating Perceptual Distance
• End-to-End Rate-Distortion Optimization for Bi-Directional Learned Video Compression
• Frank-Wolfe Network: An Interpretable Deep Structure for Non-Sparse Coding
• Low-rank Characteristic Tensor Density Estimation Part I: Foundations
• LLIC: Large Receptive Field Transform Coding with Adaptive Weights for Learned Image Compression
• Attention-Based Generative Neural Image Compression on Solar Dynamics Observatory
• Analysis of Neural Image Compression Networks for Machine-to-Machine Communication
• Recognition-Aware Learned Image Compression
• Color Learning for Image Compression
• DeepJSCC-f: Deep Joint Source-Channel Coding of Images with Feedback
• Variational Bayes image restoration with compressive autoencoders
• Neural-based Compression Scheme for Solar Image Data
• Autoencoder based image compression: can the learning be quantization independent?
• End-to-end optimization of nonlinear transform codes for perceptual quality
• Active Fine-Tuning from gMAD Examples Improves Blind Image Quality Assessment
• Slimmable Encoders for Flexible Split DNNs in Bandwidth and Resource Constrained IoT Systems
• Visual Information flow in Wilson-Cowan networks
• Learning End-to-End Lossy Image Compression: A Benchmark
• Binocular Rivalry Oriented Predictive Auto-Encoding Network for Blind Stereoscopic Image Quality Measurement
• Self-Organized Variational Autoencoders (Self-VAE) for Learned Image Compression
• Modeling Category-Selective Cortical Regions with Topographic Variational Autoencoders
• DSIC: Deep Stereo Image Compression
• Region of Interest Loss for Anonymizing Learned Image Compression
• Neural Communication Systems with Bandwidth-limited Channel
• Multiscale Augmented Normalizing Flows for Image Compression
• Deep Joint Source-Channel Coding for Multi-Task Network
• Optimizing Learned Image Compression on Scalar and Entropy-Constraint Quantization
• Simultaneous Estimation of Non-Gaussian Components and their Correlation Structure
• Generative Memorize-Then-Recall framework for low bit-rate Surveillance Video Compression