Discriminating Natural Image Statistics from Neuronal Population Codes

The power law provides an efficient description of amplitude spectra of natural scenes. Psychophysical studies have shown that the forms of the amplitude spectra are clearly related to human visual performance, indicating that the statistical parameters in natural scenes are represented in the nervous system. However, the underlying neuronal computation that accounts for the perception of the natural image statistics has not been thoroughly studied. We propose a theoretical framework for neuronal encoding and decoding of the image statistics, hypothesizing the elicited population activities of spatial-frequency selective neurons observed in the early visual cortex. The model predicts that frequency-tuned neurons have asymmetric tuning curves as functions of the amplitude spectra falloffs. To investigate the ability of this neural population to encode the statistical parameters of the input images, we analyze the Fisher information of the stochastic population code, relating it to the psychophysically measured human ability to discriminate natural image statistics. The nature of discrimination thresholds suggested by the computational model is consistent with experimental data from previous studies. Of particular interest, a reported qualitative disparity between performance in fovea and parafovea can be explained based on the distributional difference over preferred frequencies of neurons in the current model. The threshold shows a peak at a small falloff parameter when the neuronal preferred spatial frequencies are narrowly distributed, whereas the threshold peak vanishes for a neural population with a more broadly distributed frequency preference. These results demonstrate that the distributional property of neuronal stimulus preference can play a crucial role in linking microscopic neurophysiological phenomena and macroscopic human behaviors.幂律（power law）能够高效描述自然场景的振幅谱。心理物理学研究表明，振幅谱的形态与人类视觉表现显著相关，这暗示自然场景的统计参数已在神经系统中得到表征。然而，解释自然图像统计特征感知的底层神经元计算机制尚未得到充分研究。我们提出了一个用于图像统计特征神经元编码与解码的理论框架，该框架基于早期视觉皮层中观察到的空间频率选择性神经元的群体激活模式提出假设。该模型预测，频率调谐神经元的调谐曲线呈非对称形态，且随振幅谱衰减率的变化呈现特定规律。为探究该神经元群体对输入图像统计特征参数的编码能力，我们分析了随机群体编码的费舍尔信息（Fisher information），并将其与心理物理学测量得到的人类区分自然图像统计特征的能力相关联。该计算模型所揭示的辨别阈值特性与此前研究中的实验数据相符。尤为值得关注的是，已有研究报道的中央凹与副中央凹视觉表现间的质性差异，可通过本模型中神经元偏好频率的分布差异得到解释。当神经元的偏好空间频率分布较窄时，阈值在较小的衰减参数处出现峰值；而当神经元群体的频率偏好分布更宽泛时，该阈值峰值则会消失。上述结果表明，神经元刺激偏好的分布特性，在连接微观神经生理现象与宏观人类行为的过程中可发挥关键作用。