Thomson M G
Colour & Imaging Institute, University of Derby, UK.
Network. 2001 Aug;12(3):271-87.
Techniques adapted from standard higher-order statistical methods are applied to natural-image data in an attempt to discover exactly what makes 'wavelet' representations of natural scenes sparse. Specifically, this paper describes a measure known as the phase-only second spectrum, a fourth-order statistic which quantifies harmonic beat interactions in data, and uses it to show that there are statistical consistencies in the phase spectra of natural scenes. The orientation-averaged phase-only second spectra of natural images appear to show power-law behaviour rather like image power spectra, but with a spectral exponent of approximately -1 instead of -2. They also appear to display a similar form of scale-invariance. Further experimental results indicate that the form of these spectra can account for the observed sparseness of bandpass-filtered natural scenes. This implies an intimate relationship between the merits of sparse neural coding and the exploitation of non-Gaussian 'beats' structures by the visual system.
从标准高阶统计方法改编而来的技术被应用于自然图像数据，试图确切发现是什么使得自然场景的“小波”表示稀疏。具体而言，本文描述了一种称为纯相位二阶谱的度量，这是一种四阶统计量，用于量化数据中的谐波拍频相互作用，并使用它来表明自然场景的相位谱存在统计一致性。自然图像的方向平均纯相位二阶谱似乎呈现出类似图像功率谱的幂律行为，但谱指数约为 -1 而非 -2。它们似乎还表现出类似形式的尺度不变性。进一步的实验结果表明，这些谱的形式可以解释带通滤波后的自然场景中观察到的稀疏性。这意味着稀疏神经编码的优点与视觉系统对非高斯“拍频”结构的利用之间存在密切关系。
