We develop a new statistical model for photographic images, in which the
local responses of a bank of linear filters are described as jointly Gaussian,
with zero mean and a covariance that varies slowly over spatial position. We
optimize sets of filters so as to minimize the nuclear norms of matrices of
their local activations (i.e., the sum of the singular values), thus
encouraging a flexible form of sparsity that is not tied to any particular
dictionary or coordinate system. Filters optimized according to this objective
are oriented and bandpass, and their responses exhibit substantial local
correlation. We show that images can be reconstructed nearly perfectly from
estimates of the local filter response covariances alone, and with minimal
degradation (either visual or MSE) from low-rank approximations of these
covariances. As such, this representation holds much promise for use in
applications such as denoising, compression, and texture representation, and
may form a useful substrate for hierarchical decompositions.

本文提出了一种新的基于统计模型的图像描述方法，其中利用线性滤波器组的局部响应共同服从零均值的高斯分布，协方差在空间位置上变化缓慢。文章通过优化一组滤波器，以最小化其本地激活矩阵（即奇异值之和），从而鼓励一种灵活的稀疏形式，同时也使其不依赖于任何特定的词典或坐标系统，实现了图像近乎完美的重构，具有很好的噪声去除、压缩和纹理表示能力。