Design of bi-orthogonal rational discrete wavelet transform and the associated applications.
Nguyen Si Tran Nguyen · Adelaide Research & Scholarship (AR&S) (University of Adelaide) · 2014
Time-frequency analysis has long been a very useful tool in the field of signal processing, especially in dealing with non-stationary signals. Wavelet transform is amongst many time-frequency analysis techniques whose attributes have been well exploited in many classic applications such as de-noising and compression. In recent years, representation sparsity, a measure of the representation’s ability to condense signals’ energy into few coefficients, has raised much interest from researchers in many fields such as signal processing, information theory and applied mathematics due to its wide range of use. Thus, many classes of time-frequency representations have recently been developed from the conventional ones in maximising the representation sparsity recently. Rational discrete wavelet transform (RADWT), an extended class of the conventional wavelet family, is among those representations. This thesis discusses the design of bi-orthogonal rational discrete wavelet transform which is constructed from finite impulse response (FIR) two-channel rational rate filter banks and the associated potential applications. Techniques for designing the bi-orthogonal rational filter bank are proposed, their advantages and disadvantages are discussed and compared with the existing designs in literature. Experimental examples are provided to illustrate the use of the novel bi-orthogonal RADWT in application such as signal separation. The experiments show sparser signal representations with RADWTs over conventional dyadic discrete wavelet transforms (DWTs). This is then exploited in applications such as de-noising and signal separation based on basis pursuit.