Fritz Sommer gave a COSYNE 2011 workshop presentation of seemingly magical results coauthored by Guy Isely and Christopher Hillar.
Suppose an area of the brain deals in a signal which is sparse in some underlying unknown dictionary. This area subsamples the signal with say a random measurement matrix, and sends the subsampled signal to another area. The receiving area doesn't know what the original signals were, or what the underlying sparsifying dictionary was, or what the measurement matrix were; all it knows are the subsampled measurements it has received. If the receiving area learns a dictionary in which the subsampled signals it received are sparse, can this sparse representation also be used to linearly represent the original signal? The answer is yes.
To restore normality and disprove magic, read their NIPS paper. Apparently a longer paper with proofs is due to come out soon.