An Improved Infrared/Visible Fusion for Astronomical Images

An undecimated dual tree complex wavelet transform (UDTCWT) based fusion scheme for astronomical visible/IR images is developed. The UDTCWT reduces noise effects and improves object classification due to its inherited shift invariance property. Local standard deviation and distance transforms are used to extract useful information (especially small objects). Simulation results compared with the state-of-the-art fusion techniques illustrate the superiority of proposed scheme in terms of accuracy for most of the cases

A recursive scheme for computing autocorrelation functions of decimated complex wavelet subbands

This paper deals with the problem of the exact computation of the autocorrelation function of a real or complex discrete wavelet subband of a signal, when the autocorrelation function (or Power Spectral Density, PSD) of the signal in the time domain (or spatial domain) is either known or estimated using a separate technique. The solution to this problem allows us to couple time domain noise estimation techniques to wavelet domain denoising algorithms, which is crucial for the development of blind wavelet-based denoising techniques. Specifically, we investigate the Dual-Tree complex wavelet transform (DT-CWT), which has a good directional selectivity in 2-D and 3-D, is approximately shift-invariant, and yields better denoising results than a discrete wavelet transform (DWT). The proposed scheme gives an analytical relationship between the PSD of the input signal/image and the PSD of each individual real/complex wavelet subband which is very useful for future developments. We also show that a more general technique, that relies on Monte-Carlo simulations, requires a large number of input samples for a reliable estimate, while the proposed technique does not suffer from this problem

Enhanced B-Wavelets via Mixed, Composite Packets

A modified B-wavelet construction with enhanced filter characteristics is considered. The design comprises a superposition of tessellated, integer dilated, ‘sister’ wavelet functions. We here propose a cascaded filter-bank realisation of this wavelet family together with some notable extensions. We prove that modifications of low-order members exist in the multiresolution subspace spanned by the half-translates of the original wavelets and hence that the resulting modified wavelet coefficients can be computed as convolutions of the undecimated original wavelet coefficients. Finite impulse response filters are thus designed and incorporated into a B-wavelet packet architecture such that the mainlobe-to-sidelobe ratio of the resulting wavelet filter characteristic is improved. This is achieved by designing the filters so that zeros are introduced near to the maxima of the harmonics. It is shown that the numbers of zeros can be balanced with the length of the corresponding filters by controlling the ‘modification order’. Several constructions are presented. We prove that two such constructions satisfy the perfect reconstruction property for all orders. The resulting modified wavelets preserve many of the properties of the original B-wavelets such as differentiability, number of vanishing moments, symmetry, anti-symmetry, finite support, and the existence of a closed form expression

Using the Dual-Tree Complex Wavelet Transform for Improved Fabric Defect Detection

Published ArticleThe dual-tree complex wavelet transform (DTCWT) solves the problems of shift variance and low directional selectivity in two and higher dimensions found with the commonly used discrete wavelet transform (DWT). It has been proposed for applications such as texture classification and content-based image retrieval. In this paper, the performance of the dual-tree complex wavelet transform for fabric defect detection is evaluated. As experimental samples, the fabric images from TILDA, a textile texture database from the Workgroup on Texture Analysis of the German Research Council (DFG), are used. The mean energies of real and imaginary parts of complex wavelet coefficients taken separately are identified as effective features for the purpose of fabric defect detection. Then it is shown that the use of the dual-tree complex wavelet transform yields greater performance as compared to the undecimated wavelet transform (UDWT) with a detection rate of 4.5% to 15.8% higher depending on the fabric type