Mismatched Wavelets: Information Hiding and Edge Detection

Wavelets and other tight frames have been used for numerous signal and image processing applications. These transforms consist of two or more filters that are applied in "Analysis" and "Synthesis" operators. In general, these operators are designed such that perfect reconstruction is preserved. This paper introduces mismatched wavelets, in which analysis and synthesis operators do not form a perfect reconstruction system. Rather than minimize the errors introduced by such a system, the authors study and exploit these errors. These structured errors are far from random, preserving much of the informational structure of the image.