Table 1.

Theories of efficient retinal coding

Goal	Explanation	Can this account for center-surround RFs?
Compression (lossy)	To meet the reduced capacity of the optic nerve, attenuation of high spatial frequencies in periphery provides an efficient means of reducing bandwidth between photoreceptors and ganglion cells. The highest frequencies have the lowest signal-to-noise ratio given a 1/f environment and flat noise	A wide variety of transforms can achieve high-frequency attenuation
	Noise is reduced in regime where noise and signal power approach equivalence	Insufficient constraint to account for center-surround receptive fields
Decorrelation	Cells with tuning functions that rise with frequency can reduce pairwise correlations when the cells are spaced appropriately. The known tuning functions should therefore help reduce this form of statistical redundancy	Many transforms can achieve decorrelation. Even if the tuning curve was optimal for decorrelation, many possible transforms can have the same tuning curves Visual system maintains significant correlations between neighboring neurons, and these correlations may be important in development Insufficient constraint to account for center-surround RFs
Response equalization	Allows neurons of all sizes to produce the same average response to natural scenes with 1/f spectra. Predicts response magnitude of macaque P cells	A variety of transforms can sphere 1/f-distributed data Insufficient on its own to account for center-surround receptive fields or shape of tuning curves
Sparseness	Center-surround RFs are more sparse than phase- randomized RFs	Wavelet-like/oriented receptive fields can provide greater sparseness than center- surround receptive fields
Minimal size/wiring	Could achieve most sparse solution and reduce total dendritic field needed Restricts phases towards an aligned center-surround organization	A minimal wiring constraint on its own cannot produce an extended receptive field
Decorrelation + response equalization + minimal size	The combination of all three constraints may be sufficient to describe the basic sensitivity and center- surround organization	Further consideration is needed to account for known non-linearities and temporal properties

It should be emphasized that this analysis largely ignores the importance of non-linearities in retinal processing.