Academic literature on the topic 'Bi-orthogonal rational filter banks'

For some measurement and detection applications based on video (sequence images), if the exposure time of camera is not suitable with the motion speed of the photographed target, fuzzy edges will be produced in the image, and some poor lighting condition will aggravate this edge blur phenomena. Especially, the existence of noise in industrial field environment makes the extraction of fuzzy edges become a more difficult problem when analyzing the posture of a high-speed moving target. Because noise and edge are always both the kind of high-frequency information, it is difficult to make trade-offs only by frequency bands. In this paper, a noise-tolerant edge detection method based on the correlation relationship between layers of wavelet transform coefficients is proposed. The goal of the paper is not to recover a clean image from a noisy observation, but to make a trade-off judgment for noise and edge signal directly according to the characteristics of wavelet transform coefficients, to realize the extraction of edge information from a noisy image directly. According to the wavelet coefficients tree and the Lipschitz exponent property of noise, the idea of neural network activation function is adopted to design the activation judgment method of wavelet coefficients. Then the significant wavelet coefficients can be retained. At the same time, the non-significant coefficients were removed according to the method of judgment of isolated coefficients. On the other hand, based on the design of Daubechies orthogonal compactly-supported wavelet filter, rational coefficients wavelet filters can be designed by increasing free variables. By reducing the vanishing moments of wavelet filters, more high-frequency information can be retained in the wavelet transform fields, which is benefit to the application of edge detection. For a noisy image of high-speed moving targets with fuzzy edges, by using the length 8-4 rational coefficients biorthogonal wavelet filters and the algorithm proposed in this paper, edge information could be detected clearly. Results of multiple groups of comparative experiments have shown that the edge detection effect of the proposed algorithm in this paper has the obvious superiority.

This note designs two kinds of rational wavelet filter banks using three basic bricks: the finite Blaschke product, Bezout polynomial and the symbol of the cardinal B-spline. In orthogonal case, the corresponding wavelets are generalization of Daubechies’ wavelets. The role of the Blaschke product is the adjustment of the peaks of wavelet functions.

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.
Thesis (Ph.D.) -- University of Adelaide, School of Electrical and Electronic Engineering, 2014