Haft M, van Hemmen J L
Siemens AG, München, Germany.
Network. 1998 Feb;9(1):39-71.
In the first part of this paper we discuss a technical visual sensory system, which--in analogy with the retina--includes some preprocessing of visual information. In so doing, we use an information-theoretic criterion, the infomax ansatz, to optimize the response of the sensory system. In particular, it is shown that the lattice structure of the photoreceptor array has to be taken into account. By a discrete Fourier transformation on a triangular lattice we derive the frequency response of the infomax filter within the first Brillouin zone. To illustrate the response properties, infomax filters adapted to different noise levels are applied to images with different signal-to-noise ratios. This clearly demonstrates the necessity of adaptation of the filter properties to the given noise level. Furthermore, it is shown how to efficiently implement infomax-like filters by simple networks with only nearest-neighbour interactions. A two-layered network topology proves to be very advantageous in implementing the desired high-pass or low-pass properties. The network topology allows for adaption of the network to low and high noise levels by simply adjusting the nearest-neighbour couplings. In the second part of this paper, we compare the previously described information-theoretic requirements on a visual sensory system with biological facts known from the vertebrate retina. The substantial physiological response properties of the vertebrate retina are in agreement with the main features of the infomax filter. Since available experimental data lacks information which is necessary for a more quantitative comparison, we present suggestions for future experiments. Some key anatomical features of the retina of many vertebrates compare well with our two-layered implementation of the infomax filter. The analogy, in particular, concerns the adaption mechanism. To illustrate this point, we summarize some recent experiments which demonstrate that in the retina of some species adaption is based on the release of the neuromodulator dopamine by the interplexiform cells. This causes the horizontal cells to decouple. On the basis of recently gained understanding of the outer plexiform layer of the retina some further hypotheses about the functionality of the retina become obvious and possible future experiments to verify or refute them are suggested. Finally, we discuss the infomax approach from a more general point of view. In particular, we show that redundancy is essential to obtaining noise robustness of an internal representation of the environment as it is produced by a sensory system such as the retina.
在本文的第一部分，我们讨论一种技术视觉传感系统，该系统——类似于视网膜——包括一些视觉信息的预处理。在此过程中，我们使用一种信息论标准，即信息最大化假设，来优化传感系统的响应。特别地，结果表明必须考虑光感受器阵列的晶格结构。通过对三角晶格进行离散傅里叶变换，我们推导出第一布里渊区内信息最大化滤波器的频率响应。为了说明响应特性，将适应不同噪声水平的信息最大化滤波器应用于具有不同信噪比的图像。这清楚地证明了滤波器特性适应给定噪声水平的必要性。此外，还展示了如何通过仅具有最近邻相互作用的简单网络来有效地实现类似信息最大化的滤波器。事实证明，两层网络拓扑结构在实现所需的高通或低通特性方面非常有利。该网络拓扑结构允许通过简单地调整最近邻耦合，使网络适应低噪声水平和高噪声水平。在本文的第二部分，我们将前面描述的关于视觉传感系统的信息论要求与脊椎动物视网膜的生物学事实进行比较。脊椎动物视网膜的主要生理响应特性与信息最大化滤波器的主要特征一致。由于现有的实验数据缺乏进行更定量比较所需的信息，我们提出了未来实验的建议。许多脊椎动物视网膜的一些关键解剖特征与我们对信息最大化滤波器的两层实现方式比较吻合。这种类比尤其涉及适应机制。为了说明这一点，我们总结了一些最近的实验，这些实验表明在某些物种的视网膜中，适应是基于网间细胞释放神经调质多巴胺。这导致水平细胞解耦。基于最近对视网膜外网状层的理解，一些关于视网膜功能的进一步假设变得明显，并提出了未来验证或反驳这些假设的可能实验。最后，我们从更一般的角度讨论信息最大化方法。特别地，我们表明冗余对于获得由诸如视网膜这样的传感系统产生的环境内部表示的噪声鲁棒性至关重要。
