Title :
Multidimensional, mapping-based complex wavelet transforms
Author :
Fernandes, Felix C A ; van Spaendonck, R.L.C. ; Burrus, C. Sidney
Author_Institution :
Texas Instrum. Inc., Dallas, TX, USA
Abstract :
Although the discrete wavelet transform (DWT) is a powerful tool for signal and image processing, it has three serious disadvantages: shift sensitivity, poor directionality, and lack of phase information. To overcome these disadvantages, we introduce multidimensional, mapping-based, complex wavelet transforms that consist of a mapping onto a complex function space followed by a DWT of the complex mapping. Unlike other popular transforms that also mitigate DWT shortcomings, the decoupled implementation of our transforms has two important advantages. First, the controllable redundancy of the mapping stage offers a balance between degree of shift sensitivity and transform redundancy. This allows us to create a directional, nonredundant, complex wavelet transform with potential benefits for image coding systems. To the best of our knowledge, no other complex wavelet transform is simultaneously directional and nonredundant. The second advantage of our approach is the flexibility to use any DWT in the transform implementation. As an example, we exploit this flexibility to create the complex double-density DWT: a shift-insensitive, directional, complex wavelet transform with a low redundancy of (3M-1)/(2M-1) in M dimensions. No other transform achieves all these properties at a lower redundancy, to the best of our knowledge. By exploiting the advantages of our multidimensional, mapping-based complex wavelet transforms in seismic signal-processing applications, we have demonstrated state-of-the-art results.
Keywords :
discrete wavelet transforms; image coding; complex wavelet transform; directional wavelet transform; discrete wavelet transform; image coding system; mapping-based wavelet transform; multidimensional wavelet transform; seismic signal processing; shift sensitivity; shift-insensitive wavelet transform; transform redundancy; Discrete transforms; Discrete wavelet transforms; Europe; Filters; Image coding; Image processing; Instruments; Multidimensional systems; Signal processing; Wavelet transforms; Algorithms; Artificial Intelligence; Computer Graphics; Computer Simulation; Image Enhancement; Image Interpretation, Computer-Assisted; Information Storage and Retrieval; Models, Biological; Models, Statistical; Numerical Analysis, Computer-Assisted; Pattern Recognition, Automated; Reproducibility of Results; Sensitivity and Specificity; Signal Processing, Computer-Assisted;
Journal_Title :
Image Processing, IEEE Transactions on
DOI :
10.1109/TIP.2004.838701