1. An information processing apparatus comprising: synthesis filtering process means for performing a synthesis filtering process on image data, the image data having been subjected to hierarchical executions of an analysis filtering process, each execution of the analysis filtering process having caused frequency components of the image data to be divided into high-frequency components and low-frequency components, the hierarchical executions of the analysis filtering process having caused the image data to be divided into a plurality of frequency bands, the synthesis filtering process involving synthesizing frequency components of frequency bands in each division level by performing a lifting calculation; and control means for controlling an execution of the synthesis filtering process performed by the synthesis filtering process means for each lifting calculation such that the lifting calculations are performed in an order that allows image data to be produced part by part, each part including a plurality of lines, the control means controlling the execution by determining frequency components of a next highest division level to produce the part in response to a determination that the frequency components synthesized by performing the lifting calculation are not of baseband image data.