RETRACTED CHAPTER: Spectral Domain of Frames

The structure of frame multiresolution analysis (FMRA) is determined largely by the spectral domain of the associated frame scaling function. The carefully selected spectral domain of FMRA can significantly suppress narrowband noises, resulting in the derived frame representation of large-scale data that can achieve compression and noise suppression simultaneously. Therefore, in this chapter, we characterize the topological features of spectral domains of FMRAs and establish the relation between frame sets and spectral domains of frames.