Equivalence of Symmetric Pre-Extension and Lifting Step Extension in the JPEG 2000 Standard

Symmetric extension, traditionally implemented as a pre-processing step, is a popular method of handling image boundaries in subband image coding schemes. With the advent of lifting factorizations, however, a second strategy for boundary handling consists of extending the input signal's polyphase components as part of each lifting step. Both methods are employed in the ISO/IEC JPEG 2000 standard: symmetric pre- extension in Part 1 and lifting step extension in Part 2 of the standard. We present a system-level framework for analyzing both classes of schemes that can be used to prove mathematical equivalence of the two approaches.