Fig. 5

Two dictionary bases learned from overlapping patches extracted from the photograph of Park Avenue in Fig. 4. On the left, there are 32 dictionary elements and on the right 512. Dictionaries are overcomplete when they have more elements than the dimension of the signal. Overcompleteness helps induce sparsity by allowing multiple choices for representing a signal where only one is needed. In this example, the patch dimension is 8×8, so the dictionary on the right is overcomplete, but the dictionary on the leftis undercomplete or low-rank (32<64<512)