Sparse Coding of Natural Images Produces Localized, Oriented, Bandpass Receptive Fields

The images we typically view, or natural scenes, constitute a minuscule fraction of the space of all possible images. It seems reasonable that the visual cortex, which has evolved and developed to eeectively cope with these images, has discovered eecient coding strategies for representing their structure. Here, we explore the hypothesis that the coding strategy employed at the earliest stage of the mammalian visual cortex maximizes the sparseness of the representation. We show that a learning algorithm that attempts to nd linear sparse codes for natural scenes will develop receptive elds that are localized , oriented, and bandpass, much like those in the visual system. These receptive elds produce a more eecient image representation for later stages of processing because sparseness reduces the entropies of individual outputs, which in turn reduces the redundancy due to complex statistical dependencies among unit activities. The spatial receptive elds of simple cells in mammalian striate cortex have been reasonably well described physiologically and can be characterized as being localized, oriented, and bandpass: Each cell responds to visual stimuli within a restricted and contiguous region of space that is organized into excitatory and inhibitory subbelds elongated along a particular direction, and the spatial frequency response is generally bandpass with bandwidths in the range of 1-2 octaves 1, 2, 3, 4]. We seek to provide a functional explanation of these spatial response properties in terms of an eecient coding strategy for natural images. An image, I(x; y), is modeled as a linear superposition of (not necessarily orthogonal) basis functions, i (x; y):