Polarized wavelets and curvelets on the sphere

The statistics of the temperature anisotropies in the primordial cosmic microwave background radiation field provide a wealth of information for cosmology and for estimating cosmological parameters. An even more acute inference should stem from the study of maps of the polarization state of the CMB radiation. Measuring the extremely weak CMB polarization signal requires very sensitive instruments. The full-sky maps of both temperature and polarization anisotropies of the CMB to be delivered by the upcoming Planck Surveyor satellite experiment are hence being awaited with excitement. Multiscale methods, such as isotropic wavelets, steerable wavelets, or curvelets, have been proposed in the past to analyze the CMB temperature map. In this paper, we contribute to enlarging the set of available transforms for polarized data on the sphere. We describe a set of new multiscale decompositions for polarized data on the sphere, including decimated and undecimated Q-U or E-B wavelet transforms and Q-U or E-B curvelets. The proposed transforms are invertible and so allow for applications in data restoration and denoising.Comment: Accepted. Full paper will figures available at http://jstarck.free.fr/aa08_pola.pd

Numerical Issues When Using Wavelets

International audienceWavelets and related multiscale representations pervade all areas of signal processing. The recent inclusion of wavelet algorithms in JPEG 2000 – the new still-picture compression standard– testifies to this lasting and significant impact. The reason of the success of the wavelets is due to the fact that wavelet basis represents well a large class of signals, and therefore allows us to detect roughly isotropic elements occurring at all spatial scales and locations. As the noise in the physical sciences is often not Gaussian, the modeling, in the wavelet space, of many kind of noise (Poisson noise, combination of Gaussian and Poisson noise, long-memory 1/f noise, non-stationary noise, ...) has also been a key step for the use of wavelets in scientific, medical, or industrial applications [1]. Extensive wavelet packages exist now, commercial (see for example [2]) or non commercial (see for example [3, 4]), which allows any researcher, doctor, or engineer to analyze his data using wavelets

Ground penetrating Radar Clutter Removal via 1D Fast Sub band Decomposition

Target detection performance in ground-penetrating radar (GPR) deteriorates highly in the presence of clutter. Multi-scale (wavelet transform) or the recently proposed multi-scale and multi-directional decomposition based methods can efficiently remove the clutter, however they have high computational complexity. In this paper, we propose a new multi-scale method which requires only 1D fast subband decomposition of the rows of the GPR image. The resulting detail layers directly provide the clutter-free target component of the GPR image. The proposed method is compared to the state-of-art clutter removal methods both visually and quantitatively using a realistic simulated dataset which is constructed by the gprMax simulation software. The results show that the proposed 1D subband decomposition scheme approximates the classical 2D wavelet decomposition successfully and even presents a performance increase as well as a complexity decrease for fast decomposition methods based on lifting wavelet transform and a trous wavelet transform

Texture-adaptive mother wavelet selection for texture analysis

Classification results obtained using wavelet-based texture analysis techniques vary with the choice of mother wavelet used in the methodology. We discuss the use of mother wavelet filters as parameters in a probabilistic approach to texture analysis based on adaptive biorthogonal wavelet packet bases. The optimal choice for the mother wavelet filters is estimated from the data, in addition to the other model parameters. The model is applied to the classification of single texture images and mosaics of Brodatz textures, the results showing improvement over the performance of standard wavelets for a given filter length

Survey on wavelet based image fusion techniques

Image fusion is the process of combining multiple images into a single image without distortion or loss of information. The techniques related to image fusion are broadly classified as spatial and transform domain methods. In which, the transform domain based wavelet fusion techniques are widely used in different domains like medical, space and military for the fusion of multimodality or multi-focus images. In this paper, an overview of different wavelet transform based methods and its applications for image fusion are discussed and analysed

Vector extension of monogenic wavelets for geometric representation of color images

14 pagesInternational audienceMonogenic wavelets offer a geometric representation of grayscale images through an AM/FM model allowing invariance of coefficients to translations and rotations. The underlying concept of local phase includes a fine contour analysis into a coherent unified framework. Starting from a link with structure tensors, we propose a non-trivial extension of the monogenic framework to vector-valued signals to carry out a non marginal color monogenic wavelet transform. We also give a practical study of this new wavelet transform in the contexts of sparse representations and invariant analysis, which helps to understand the physical interpretation of coefficients and validates the interest of our theoretical construction

Lifting dual tree complex wavelets transform

We describe the lifting dual tree complex wavelet transform (LDTCWT), a type of lifting wavelets remodeling that produce complex coefficients by employing a dual tree of lifting wavelets filters to get its real part and imaginary part. Permits the remodel to produce approximate shift invariance, directionally selective filters and reduces the computation time (properties lacking within the classical wavelets transform). We describe a way to estimate the accuracy of this approximation and style appropriate filters to attain this. These benefits are often exploited among applications like denoising, segmentation, image fusion and compression. The results of applications shrinkage denoising demonstrate objective and subjective enhancements over the dual tree complex wavelet transform (DTCWT). The results of the shrinkage denoising example application indicate empirical and subjective enhancements over the DTCWT. The new transform with the DTCWT provide a trade-off between denoising computational competence of performance, and memory necessities. We tend to use the PSNR (peak signal to noise ratio) alongside the structural similarity index measure (SSIM) and the SSIM map to estimate denoised image quality