In previous work (Olshausen & Field 1996), an algorithm was described
for learning linear sparse codes which, when trained on natural images,
produces a set of basis functions that are spatially localized, oriented,
and bandpass (i.e., wavelet-like). This note shows how the algorithm may
be interpreted within a maximum-likelihood framework. Several useful insights
emerge from this connection: it makes explicit the relation to statistical
independence (i.e., factorial coding), it shows a formal relationship to
the algorithm of Bell and Sejnowski (1995), and it suggests how to adapt
parameters that were previously fixed.