Tunable Q-factor 2-D Discrete Wavelet Transformation Filter Design And Performance Analysis

Q인자 조절 가능 2차원 이산 웨이브렛 변환 필터의 설계와 성능분석

  • 신종홍 (숭실사이버대학교 융합정보보안학과)
  • Received : 2015.02.22
  • Accepted : 2015.03.11
  • Published : 2015.03.30


The general wavelet transform has profitable property in non-stationary signal analysis specially. The tunable Q-factor wavelet transform is a fully-discrete wavelet transform for which the Q-factor Q and the asymptotic redundancy r, of the transform are easily and independently specified. In particular, the specified parameters Q and r can be real-valued. Therefore, by tuning Q, the oscillatory behavior of the wavelet can be chosen to match the oscillatory behavior of the signal of interest, so as to enhance the sparsity of a sparse signal representation. The TQWT is well suited to fast algorithms for sparsity-based inverse problems because it is a Parseval frame, easily invertible, and can be efficiently implemented. The transform is based on a real valued scaling factor and is implemented using a perfect reconstruction over-sampled filter bank with real-valued sampling factors. The transform is parameterized by its Q-factor and its over-sampling rate, with modest over-sampling rates being sufficient for the analysis/synthesis functions to be well localized. This paper describes filter design of 2D discrete-time wavelet transform for which the Q-factor is easily specified. With the advantage of this transform, perfect reconstruction filter design and implementation for performance improvement are focused in this paper. Hence, the 2D transform can be tuned according to the oscillatory behavior of the image signal to which it is applied. Therefore, application for performance improvement in multimedia communication field was evaluated.


  1. I. W. Selesnick, "Sparse signal representations using the tunable Q-factor wavelet transform," In Proceedings of SPIE, Vol. 8138 (Wavelets and Sparsity XIV), 2011.
  2. 신종홍, "3중 밀도 이산 웨이브렛 변환을 이용한 디지털 영상 처리 기법," 디지털산업정보학회논문집, 제8권, 제3호, 2012, pp. 131-143.
  3. I. W. Selesnick, "Wavelet transform with tunable Q-factor," IEEE Trans. on Signal Processing. Vol. 59, No. 8, 2011, pp. 3560-3575.
  4. P. P. Vaidynathan, "Multirate digital filters, filter banks, polyphase network and applications: A Tutorial," Proceedings of the IEEE. Vol. 78, No. 1, 1990.
  5. Jingyu Yang, Yao Wang, "Image Coding Using DualTree Discrete Wavelet Transform," IEEE Trans. on Image Processing, Vol. 17, No. 9, 2008, pp. 1555-1569.
  6. 신종홍, "Q인자의 조절이 가능한 이산 웨이브렛 변환을 이용한 디지털 영상 처리 기법," 디지털산업정보학회논문집, 제10권, 제3호, 2014, pp. 237-247.