Ten lectures on wavelets
Genetic Algorithm Wavelet Design for Signal Classification
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Convex Optimization
Three-dimensional shape recovery from focused image surface
ICASSP '99 Proceedings of the Acoustics, Speech, and Signal Processing, 1999. on 1999 IEEE International Conference - Volume 06
ICPR '10 Proceedings of the 2010 20th International Conference on Pattern Recognition
IEEE Transactions on Signal Processing - Part II
IEEE Transactions on Signal Processing
A new class of two-channel biorthogonal filter banks and waveletbases
IEEE Transactions on Signal Processing
Wavelets and filter banks: theory and design
IEEE Transactions on Signal Processing
A generalized parametric PR-QMF design technique based on Bernsteinpolynomial approximation
IEEE Transactions on Signal Processing
SDP Approximation of a Fractional Delay and the Design of Dual-Tree Complex Wavelet Transform
IEEE Transactions on Signal Processing
Image quality assessment: from error visibility to structural similarity
IEEE Transactions on Image Processing
Optimal Design of FIR Triplet Halfband Filter Bank and Application in Image Coding
IEEE Transactions on Image Processing
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Traditional maximally flat wavelet filters are highly regular but suffer from poor frequency-selectivity because of their wide transition band. In this paper, an efficient method is proposed for the design of biorthogonal perfect reconstruction wavelet filter banks, known as halfband-pair filter banks (HPFB), to be used in several applications in image processing and pattern recognition. The formulation is based on representation of a general halfband polynomial in the variable x. We first derive filter coefficients in the polynomial domain (in the variable x) in terms of the coefficients of the corresponding function in z-domain. Using convex optimization techniques, and due to the simple structure of a parametric polynomial in general, we can impose some free parameters to provide a tuning opportunity to optimize and control the wavelet filter characteristics. Perfect reconstruction and desired number of vanishing moments (NVM) are incorporated into the design procedure. The method is systematic, renders a reasonable optimization problem, and it offers wavelet filters ranging from the maximally flat to the sharpest transition band. Therefore, it can provide a useful design tool, with a fine-tuning option, which is required in many applications such as watermarking, detection, segmentation, fusion, denoising, and feature extraction. The application of the wavelet pairs, which have sharper transition band and better frequency-selectivity, is shown in multifocus imaging to obtain a fully focused image from a set of registered input images at varying foci by employing the distance transform and exponentially decaying function on the subbands in the wavelet domain. Various images are tested and experimental results compare favorably to the results in the literature.