18th April 2007
As far as I can see, the paper nowhere states the rather crucial point that the even and odd receptive fields effectively sample uncorrelated noise on the retina. Thus, in eqs. (14) and (16), the two epsilons represent different, independent draws from a standard normal distribution. Thanks to Lianqing Yu, whose questions about the derivation of eq. (18) made me realise this omission.
I’ve now inspected eq. (18) more closely. It looks to me as if there is an error in the printed version. C~K1/2 should be C~K1/8 throughout. Also, the factor of 2pi in the initial normalisation should be 16pi. As far as I can tell, this does not affect the results. The normalisation (2 vs 16 pi) does not affect anything anyway, and was not even incorporated into the code. For the K1/2 vs K1/8, it’s hard to be 100% sure at this distance but as far as I can tell by looking at my records of the programs, the expression used in the code was correct. Thus, my belief is that the simulations were run with the correct expressions but the printed version was wrong.