A number of recent attempts have been made to describe early sensory coding in terms of a general information processing strategy. In this paper, two strategies are contrasted. Both strategies take advantage of the redundancy in the environment to produce more effective representations. The first is described as a “compact” coding scheme. A compact code performs a transform that allows the input to be represented with a reduced number of vectors (cells) with minimal RMS error. This approach has recently become popular in the neural network literature and is related to a process called Principal Components Analysis (PCA). A number of recent papers have suggested that the optimal “compact” code for representing natural scenes will have units with receptive field profiles much like those found in the retina and primary visual cortex. However, in this paper, it is proposed that compact coding schemes are insufficient to account for the receptive field properties of cells in the mammalian visual pathway. In contrast, it is proposed that the visual system is near to optimal in representing natural scenes only if optimality is defined in terms of “sparse distributed” coding. In a sparse distributed code, all cells in the code have an equal response probability across the class of images but have a low response probability for any single image. In such a code, the dimensionality is not reduced. Rather, the redundancy of the input is transformed into the redundancy of the firing pattern of cells. It is proposed that the signature for a sparse code is found in the fourth moment of the response distribution (i.e., the kurtosis). In measurements with 55 calibrated natural scenes, the kurtosis was found to peak when the bandwidths of the visual code matched those of cells in the mammalian visual cortex. Codes resembling “wavelet transforms” are proposed to be effective because the response histograms of such codes are sparse (i.e., show high kurtosis) when presented with natural scenes. It is proposed that the structure of the image that allows sparse coding is found in the phase spectrum of the image. It is suggested that natural scenes, to a first approximation, can be considered as a sum of self-similar local functions (the inverse of a wavelet). Possible reasons for why sensory systems would evolve toward sparse coding are presented.