We believe that a systematic effort to turn this view upside down can have major benefits. Redundant representations in a time-frequency or multiresolution setting have come up in a variety of settings. By allowing redundancy, one can enable translation invariance, modulation invariance, direction invariance, and thereby avoid such artifacts.
Redundant representations are far easier to construct that nonredundant ones.
This means that in attacking a new problem area, it is a better strategy to build a redundant representation than a nonredundant one. This a form of nonlinearity since the best representation will depend on the data. The success of many specific algoirthms in data processing stem from the flexibility provided by this nonlinearity. There are even settings in which nonredundant representations don't exist. A few examples of such frames are given in the following figure.