Density Modeling of Images using a Generalized Normalization Transformation
Johannes Ballé, Valero Laparra、Eero P. Simoncelli Center for Neural Science New York University New York, NY 10004, USA EPS is also affiliated with the Courant Institute of Mathematical Sciences at NYU; VL is also affiliated with the University of València, Spain.
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 m
中文速览
自然图像的统计规律非常复杂，直接建模其概率密度一直是个难题。研究者提出了一种名为"广义除法归一化"（Generalized Divisive Normalization，GDN）的参数化非线性变换：先对图像局部像素块做线性变换，再用一个带可学习权重和指数的池化活动量对每个响应分量做归一化，目标是让变换后的输出尽可能接近标准正态分布（即"高斯化"），所有参数均通过最小化输出的负熵在自然图像数据库上端到端优化。实验表明，GDN显著优于ICA和径向高斯化等传统方法，变换后各分量之间的互信息更低，并且由于变换可微且可高效求逆，它直接构成一个图像密度模型——从中采样出的图像块在视觉上与真实自然图像高度相似，还可作为先验概率用于图像去噪。更重要的是，将多个GDN层逐层叠加、每层用同一高斯化目标优化，自然形成一种无监督训练深度网络的框架，为理解深度神经网络中的归一化操作提供了理论依据。
原文 arXiv:1511.06281;中英对照 + 大白话阅读 https://aha.fim.ai/paper/1511.06281v4